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PHILOSOPHICAL 



TRANSACTIONS 



OF THE 



KOYAL SOCIETY OF LONDON 



SERIES A. 



CONTAINING PAPEKS OF A MATHEMATICAL 01! PHYSICAL CHAKACTER. 



VOL. 209. 



i^>r 

LONDON: ^ \ 

PRINTED BY HARRISON AND SONS, ST. MARTIN'S LANE, W.C., 

|)rmltrs in rbinarg ID is Pajtslg. 

OCTOBEB, 1909. 



\ V- 



V 

V 



6? 



v.20? 



CONTENTS. 

(A) 
VOL. 209. 



List of Illustrations page vi 

Advertisement vii 



I. On the Atomic Weight of Chlorine. By EDWARD C. EDGAR, D.Sc., the University, 
Manchester. Communicated by Prof. H. B. DIXON, F.R.S 



II. On Scandium. By Sir WILLIAM CROOK ES, D.Sc., F.R.S. ...... 15 

III. The Spectrum of Scandium, and its Relation to Solar Spectra. By A. FOWLER, 

A.R.C.S., F.R.A.S., Assistant Professor of Physics, Imperial College of 
Science and Technology, South Kensington. Communicated by Sir WILLIAM 
CEOOKES, D.Sc., F.R.S. . . . . : ............ 47 

IV. On the Nature of the Streamers in the Electric Spark. By S. R. MILNER, 

D.Sc. (Lond.), Lecturer in Physics in the University of Slicffield. Communi- 
cated by Prof. W. M. RICKS, F.R.S. ............ 71 

V. Eutectic Research. No. 1. The Alloys of Lead and Tin. By WALTER ROSEN- 

HAIN, B.A., B.C.E., ivith P. A. TUCKER. (From the National Physical 
Laboratory.) Communicated by R. T. GLAZEBROOK, M.A., F.R S. . . 89 

VI. The Emission and Transmission of Rontgen Rays. By G. W. C. KAYE, B.A. 

(Cantab.}, B.Sc. (Lond.}, A.R.C.Sc., Associate-Member of the Institution of 
Electrical Engineers, Trinity College, Cambridge. Communicated by Prof. 
J. J. THOMSON, F.R.S. ................ 123 

a 2 



VII. Memoir on the Theory of the Partitions of Numbers. Part IV. On the 

Probability that the Successful Candidate, at an Election by Ballot may 
never at any time have Fewer Votes than the One who is Unsuccessful ; on a 
Generalization of this Question; and on its Connexion with other Questions of 
Partition, Permutation, and Combination. By. Major P. A. MAcMAHON, 
F.R.S. page 153 

VIII. On the Osmotic Pressures of Aqueous Solutions of Calcium Ferrocyanide. 
Part I. Concentrated Solutions. By the EARL OF BERKELEY, F.R.S., E. G. J. 
HARTLEY, B.A. (Oxon.), and C. V. BURTON, D.Sc. (Lond.) 177 

IX. The Effect of Pressure upon Arc Spectra. No. 2. Copper, X 4000 to \ 4600. 

B/i W. GEOFFREY DUFFIELD, D.Sc., Honorary Research Fellow in Physics at 
the University of Manchester, Mackinnon Student of the Royal Society. 
Communicated by Prof. E. K.UTHERFORD, F.R.S. 205 

X. Results of Magnetic Observations at Stations on the Coasts of the British Isles, 

lit 07. By Commander L. W. P. CHETWYND, R.N., Superintendent of Com- 
passes. Communicated by Rear-Admiral A. M. FIELD, F.R.S. . . . 227 

XI. The Mobilities of the Ions produced by Rontgen Rays in Gases and Vapours. 

By E. M. WELLISCH, M.A. (Sydney], Emmanuel College, Cambridge; Barker 
Graduate Scholar of the University of Sydney. Communicated by Prof. Sir 
J. J. THOMSON, F.R.S. 249 

XII. Determination of the Surface-Tension of Water bi/ the Method of Jet Vibi*ation. 

By N. BOHR, Copenhagen. Communicated by Sir WILLIAM KAMSAY, K.C.B., 
F.R.S. 281 

XIII. On the Osmotic Pressures of Calcium Ferrocyanide Solutions. Part II. Weak 
Solutions. By the EARL OF BERKELEY, F.R.S., E. G. J. HARTLEY, B.A. 
(Oxon.), and J. STEPHENSON, B.Sc. (Lond.) 319 

XIV. On the Spontaneous Crystallisation of Monochloracetic Acid and its Mixtures 
with Naphthalene. By Principal HENRY A MIERS, F.R.S., and Miss 
FLORENCE ISAAC, Research Fellow of Somerville College, Oxford . . . 337 

XV. On the Electricity of Rain and its Origin in Thunderstorms. By GEORGE C. 

SIMPSON, D.Sc. Communicated by Dr. GILBERT T. WALKER, F.R.S. . 379 



XVI. Functions of Positive and Negative Type, and their Connection ivith the Theory 

of Integral Equations. By J. MERCER, B.A., Trinity College, Cambridge. 
Communicated by Prof. A. R FORSYTE, Sc.D., LL.D., F.R.S. . . page 415 

XVII. The Spectrum of Magnesium Hydride. By A. FOWLER, A.R.C.S., F.K.A.S., 
Assistant Professor of Physics, Imperial College of Science and Technology, 
South Kensington. Communicated by Prof. H. L. CALLENDAR, M.A., LL.D., 
F.R.S. 447 

Index to Volume 479 



[ vi ] 



LIST OF ILLUSTRATIONS. 

Plate 1. Sir WILLIAM CROOKES on Scandium. 

Plates 2-4. Dr. S. R. MILNER on the Nature of the Streamers in the Electric Spark. 

Plates 5-9. Messrs. WALTER ROSENHAIN and P. A. TUCKER : Eutectic Research. 
No. 1. The Alloys of Lead and Tin. 

Plates 10, 11. Dr. W. GEOFFREY DUFFIELD on the Effect of Pressure upon Arc 
Spectra. No. 2. Copper, X 4000 to X 4600. 

Plates 12, 13. Prof. A. FOWLER on the Spectrum of Magnesium Hydride. 



Vll 



ADVERTISEMENT, 



THE Committee appointed by the Royal Society to direct the publication of the 
Philosophical Transactions take this opportunity to acquaint the public that it fully 
appears, as well from the Council-books and Journals of the Society as from repeated 
declarations which have been made in several former Transactions, that the printing of 
them was always, from time to time, the single act of the respective Secretaries, till 
the Forty-seventh Volume ; the Society, as a Body, never interesting themselves any 
further in their publication than by occasionally recommending the revival of them to 
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Transactions had happened for any length of time to be intermitted. And this seems 
principally to have been done with a view to satisfy the public that their usual 
meetings were then continued, for the improvement of knowledge and benefit of 
mankind : the great ends of their first institution by the Royal Charters, and which 
they have ever since steadily pursued. 

But the Society being of late years greatly enlarged, and their communications more 
numerous, it was thought advisable that a Committee of their members should be 
appointed to reconsider the papers read before them, and select out of them such as 
they should judge most proper for publication in the future Transactions ; which was 
accordingly done upon the 26th of March, 1752. And the grounds of their choice are, 
and will continue to be, the importance and singularity of the subjects, or the 
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upon any subject, either of Nature or Art, that comes before them. And therefore the 
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And therefore it is hoped that no regard will hereafter be paid to such reports and 
public notices ; which in some instances have been too lightly credited, to the 
dishonour of the Society. 



PHILOSOPHICAL TRANSACTIONS. 



I. On the Atomic Weight of Chlorine. 
By EDWARD C. EDGAR, D.Sc., the University, Manchester. 

Communicated \>y Prof. H. B. DIXON, F.R.S. 

* 

Received and Read June 25, 1908. 

PART I. GENERAL. 

Six years ago Prof. DIXON and I began a research with the object of determining 
directly the weight of chlorine which combines with the unit weight of hydrogen. 
Our method was to burn a jet of hydrogen in an atmosphere of chlorine; hydrogen 
being stored and weighed in palladium, the chlorine being condensed and weighed as 
liquid. The figure we obtained for the combining weight of chlorine was appreciably 
higher than that found indirectly by STAS, and still higher than that approved by the 
International Committee on Atomic Weights. 

While this research was in progress, other determinations had been made bearing 
on the relative weights of silver, chlorine and nitrogen, so that some modification in 
the accepted values of one or more of these elements appeared inevitable. The direct 
"joining up" of the two ends of the chain connecting hydrogen with chlorine thus 
became a matter of immediate importance. Since the method of burning one gas in 
an atmosphere of the other had been proved to be accurate within fairly narrow 
limits, I was encouraged to continue the investigation, and to modify the apparatus 
with a view to eliminate some of the possible sources of error in the former series of 
experiments. 

The most important source of error lies in the weighing of the hydrogen. To 
diminish this error the weight of hydrogen employed was doubled ; and since 
Prof. DIXON and I found, when water was used to condense the hydrogen chloride 
formed in the flame, that some of the water vapour was decomposed by the free 
chlorine, I avoided this by burning a jet of chlorine in dry hydrogen, condensing the 
hydrogen chloride as it was formed in a tube dipped into liquid air. In some of the 
experiments the hydrogen chloride has been weighed. My experiments (concluded in 
1907) agree closely with the results previously obtained in 1905. 

The method employed was briefly as follows : 

Hydrogen, made by the electrolysis of barium hydrate solution and dried by potash 
and phosphorus pentoxide, was occluded and weighed in palladium contained in a 

VOL. CCIX. A 441. B 28.10.08 



2 DE. EDWARD C. EDGAR ON THE ATOMIC WEIGHT OF CHLORINE, 

boro-silicate glass bulb : the chlorine, prepared by electrolysing fused silver chloride 
in a Jena glass vessel, was weighed as a liquid in a thick-walled boro-silicate glass 
bulb; These bulbs were attached to a quartz combustion vessel, which was also 
Connected with a quartz tube and with a steel bomb and a pump. After a thorough 
evacuation of the whole apparatus, the combustion vessel was filled with hydrogen 
from the heated palladium bulb, and the chlorine was ignited by a spark at the tip of 
a quartz jet and continued to burn in the atmosphere of hydrogen, with a fine needle- 
shaped flame, until nearly all the chlorine weighed had been burnt. The hydrogen 
chloride, immediately after its formation in the flame, was condensed as a snow-white 
solid by liquid air surrounding a limb of the combustion vessel ; and a little chlorine, 
which had escaped burning, was also solidified. At the end of the combustion, the 
residual gas in the combustion vessel was extracted by the pump and subsequently 
analysed ; it proved to be practically pure hydrogen. 

Then the snow-white hydrogen chloride was allowed to pass through a quartz tube 
filled with mercury vapour, and the purified gas was condensed in a steel bomb 
immersed in liquid air. It "was successfully weighed in three experiments ; in two 
other experiments the gas was absorbed by water and weighed as aqueous acid. 

The balance was made specially for this work by Oertling. Each piece of 
apparatus weighed was tared with another of the same material and of very nearly 
equal volume and weight, and the small weights used in the weighings were reduced 
to a vacuum standard. 

Below are set out the corrected weights of hydrogen and chlorine burnt in eight 
experiments and the weights of hydrogen chloride caught in five. 

TABLE I. 





Hydrogen 
Imrnt, in 
grammes. 


Chlorine 
burnt, in 
grammes. 


Hydrogen 
chloride caught, 
in grammes. 


Chlorine burnt 


Hydrogen chloride caught 
- hydrogen burnt 


Hydrogen burnt 


Hydrogen burnt 


1 


2-1452 


75-5026 


77-6469 


35-196 


35-196 


2 


2-0387 


71-7504 


73-7880 


35-194 


35-194 


3 


1-7762 


62-5004 




35-188 




4 


1-9935 


70-1638 


72-1565 


35-196 


35-196 


5 


1-6469 


57-9671 




35-198 




6 


2-1016 


73-9662 




35-195 




7 


1-7254 


60-7162 


62-4401 


35-190 


35-189 


8 


2-0885 


73-4991 


75-5859 


35-192 


35-191 


Mean . 


35-194 + 0-0008 


35- 193 0-0009 



If the atomic weight of hydrogen be taken as 1-00762, the mean values for the 
atomic weight of chlorine calculated from the numbers in the table above are 
35'4620-0008 and 35'4610'0009. 



DR. EDWARD C. EDGAR ON THE ATOMIC WEIGHT OF CHLORINE. 3 

DIXON and EDGAR, burning hydrogen in chlorine, found the equivalent of chlorine 
to be 35'4630'0019 from their nine experiments. 

The concordance of the two sets of experiments is thus exceedingly close, and the 
number 35'462 may be taken as representing the result of the whole work'. 

On the other hand, NOTES and WEBER* have recently effected a complete 
quantitative synthesis of hydrogen chloride by passing a known weight of hydrogen 
over weighed potassium chlorplatinate, noting the loss in weight of the salt, and 
condensing and weighing in water the hydrogen chloride formed. The mean number 
they have thus obtained for the atomic weight of chlorine is 35'4520 - 0008 
(H = 1-00762). 

In view of the promised recalculation of the Atomic Weights by the International 
Committee, I have not attempted to correlate my results with the recent determi- 
nations of silver, nitrogen and chlorine. 

The inception of this work is due to Prof. DIXON, and I gladly take this opportunity 
of thanking him for the searching, yet kindly, criticism to which he has subjected 
these experiments. 

To the Government Grant Committee I am indebted for two grants, which have 
largely covered the cost of the apparatus employed. 

PART II. DETAILS OF EXPERIMENTS. 

1. Preparation of Hydrogen. The preparation of hydrogen and its occlusion in 
palladium have been fully described in the previous paper, t The only alterations I 
introduced in the arrangement of the apparatus were these : Four phosphorus 
pentoxide drying tubes instead of three were used, and a water reservoir was attached 
to one arm of the electrolysis vessel. The whole apparatus, including the bulb 
containing palladium, was made of boro-silicate glass. 

In the preparation of the hydrogen, the gas passed through two U tubes containing 
platinised pumice, kept at 400 C., instead of 220 C., to remove any oxygen diffusing 
from the + electrode. 

The purity of the hydrogen is evidenced by the fact that the residual gases from 
the combustion of all the hydrogen about 15^ grammes burnt in my eight 
experiments and of the corresponding weight of chlorine yielded less than half a cubic 
centimetre of nitrogen. If it be assumed that all this nitrogen came from the 
hydrogenised palladium bulb (which is not likely), the maximum weight of nitrogen 
present in the hydrogen was 1 part in 25,000. 

2. The Palladium Bulb. The palladium bulb, of which a sketch is given in fig. 1, 
differed little from that described in the former paper. It was made of boro-silicate 
glass, and terminated, not in a jet, but in the inner portion of a ground joint. 

* 'Jour. Amer. Chem. Soc.,' 30, 13, 1908. 
t 'Phil. Trans.,' 1906, vol. 205, p. 172. 
B 2 



4 DE. EDWAED C. EDGAE ON THE ATOMIC WEIGHT OF CHLOEINE. 

The bulb contained over 600 grammes of palladium, in which about 2% grammes 
of hydrogen were stored in each experiment. 




Fig. 1. 

To Messrs. Johnson and Matthey my thanks are due for lending me 400 grammes 
of palladium. 

3. Preparation of Chlorine. The details of the preparation of chlorine by electro- 
lysing fused silver chloride are given fully on pp. 177-180 of DIXON and EDGAR'S 
paper.* The only alteration I made in these experiments was to substitute boro-silicate 
glass for soft glass as the material for the various connecting tubes. 

As before, the purity of the gas was shown by its complete absorption by pure, 
dry mercury. 

4. The Chlorine JBirfb. The bulb, in which chlorine was condensed as a solid by 
liquid air, was made of boro-silicate glass ; a sketch of the apparatus is given in fig. 2. 




Fig. 2. 

The only difference to be noted between the apparatus I used and that described in 
the former paper is that mine terminated in a quartz jet F connected by a ground 
joint with the delivery tube. 

The " reversed " tap (e, fig. 2) had proved so trustworthy in controlling the exit of 

* 'Phil. Trans.,' 1906, vol. 205, p. 177. 



DR. EDWARD C. EDGAR ON THE ATOMIC WEIGHT OF CHLORINE. 5 

chlorine under pressure in the former experiments that it was employed unhesitatingly 
in these. 

The weights of chlorine condensed in each experiment varied between 70 and 
80 grammes. 

5. The Method of Weighing. For the various weighings I used a short-armed 
halance made specially for this work by Oertling. Even in weighing the steel bomb 
(weighing considerably over 1000 grammes) the concordance of individual weighings 
showed that their mean could be relied on to O'OOOl gramme. 

Each piece of apparatus weighed was counterpoised by another of the same material, 
and of very nearly the same volume and weight. The weights employed, though they 
had been standardised for the previous work, were carefully re-standardised for this ; 
but the variations found were too insignificant to affect results calculated from the 
older values. 

The details of the method of weighing are given in full in the former paper. It may 
be noted here that the variations in volume of the palladium bulb, caused by the 
differences in sealing off the thick-walled capillary tube, were small. In all the 
experiments the bulb and its counterpoise differed so little in volume that, though the 
density of the air in some of the determinations altered appreciably between the first 
and second weighings of the bulb, in no case was it found necessary to apply a 
correction to the apparent weight. 

6. The Combustion Appa/ratus. The chlorine was burnt in the quartz combustion 
vessel A (shown in fig. 3, and, on a larger scale, in fig. 4), a prominent feature of 




Fig. 3. 

which was the dependent vertical limb B in which hydrogen chloride could be 
condensed. The vessel had a capacity of 350 c.c. and was fitted with five ground 



6 DR. EDWARD C. EDGAR ON THE ATOMIC WEIGHT OF CHLORINE. 

quartz tubulures. Into the two small tubulures C and C t (shown both in fig. 3 and 
fig. 4) were fitted two platinum wires D and Dj, sheathed in glass except for their 
extreme tips ; these sheaths were ground into the tubulures and the joints protected 




Fig. 4. 



by caps containing mercury. By passing sparks between the tips of the wires, the 
chlorine, from the chlorine condensation bulb E (fig. 3), could be ignited easily at the 
tip of the quartz jet F. The bulb E and the palladium bulb L were connected with A 
by the ground tubulures J and K respectively. 



JL-5? 

M^ 





Fi g- 5. Fig. 6. 

7. The Evacuation Apparatus. To the tubulure M was attached, by a ground 
joint, the evacuation apparatus. This consisted of a quartz tube Q (shown in fig. 3 



DR. EDWARD C. EDGAR ON THE ATOMIC WEIGHT OF CHLORINE. 



and, on a larger scale, in fig. 5) in which mercury could be heated to absorb chlorine, 
R, a small spiral condenser, X, a nickel-plated steel tube in which to condense the 
hydrogen chloride, and side tubes leading to two manometers, P and T, and to two 
Sprengel pumps. 

In order to weigh the chlorine condenser separately, two taps, n and r, were 
inserted, and ground-glass joints fitted at N and S. The ground-glass joint S led to 
the apparatus in which hydrogen chloride was condensed and weighed. 

In six experiments this was a weighed nickel-plated steel bomb, consisting of a 
cylindrical steel tube X (fig. 6), connected by a length 
of flexible copper tubing Avith a screw valve W. 
The bomb was connected to the rest of the appa- 
ratus by the joint V a joint between glass and 
steel cemented by solid phosphoric acid. 

In two other experiments the hydrogen chloride 
was absorbed and weighed in water. Fig. 7 is a 
sketch of the apparatus used. Y was a boro-silicate 
glass bulb (over 200 c.c. in capacity), fused to which 
was a tap y and a phosphorus pentoxide tube to 
absorb water vapour. Z was a thick-walled capillary 
tube in which hydrogen chloride could be condensed 
by liquid air. A tap z closed the apparatus. 

Metaphosphoric acid was used as a lubricant on 
all the taps and ground joints. It is somewhat 
troublesome to spread evenly on a glass surface, but it has none of the disadvantages 
of organic lubricants. 

8. Method of carrying out the Combustion and Condensation. When the palladium 
bulb, the liquid chlorine bulb, the chlorine condenser, and the hydrogen chloride 
condenser had been weighed, the different parts of the combustion and condensation 
apparatus were fitted together. Then the pumps, fitted with McLeod gauges, were 
set working so as to evacuate the combustion vessel A (fig. 3) through the connecting 
tube m and the rest of the apparatus through t. Since the quartz tube Q and the 
steel bomb X had been previously evacuated prior to weighing, it was only necessary 
to evacuate the small portion between V and r. So as to facilitate the removal of 
traces of nitrogen, most of the glass apparatus was heated by the flame of a Bunsen 
burner. 

When the pressure had fallen as low as some thousandths of a millimetre of 
mercury, the now vacuous combustion vessel was isolated from the pump by closing a 
tap, and the lower end of the vertical limb B was immersed in liquid air. 

The liquid chlorine bulb E was packed into a freezing mixture of calcium chloride 
and ice, in which it was kept during the combustion. 

The palladium bulb L, enclosed in an asbestos-lined copper box, was gradually raised 




Fig. 7. 



8 DR. EDWARD C. EDGAR ON THE ATOMIC WEIGHT OF CHLORINE. 

to 250 C. Then hydrogen was cautiously admitted through the tap / until the 
pressure shown by the manometer P was nearly atmospheric, at which point I was 

temporarily closed. 

The glass cul-de-sac H was broken by lifting the small piece of steel rod G, 
imbedded in glass, by means of an electromagnet, and allowing it to drop. Since the 
temperature of the liquid chlorine was about -25 C., the pressure on the reversed 
tap e was rather more than atmospheric. The ignition of chlorine at the tip of the 
quartz jet F was brought about by cautiously turning the tap e so as to admit chlorine 
to F, at the same time rapidly passing sparks between the platinum tips until the 
gas had lit. Chlorine burns in dry hydrogen with a fine needle-shaped flame. In 
daylight this cannot easily be seen ; the combustion therefore was carried out in a 
dark room. The only part of the combustion vessel A heated by the burnt gases 
was the end immediately opposite the flame ; during the combustion this was 
continuously cooled by a. rapid stream of water. The atmosphere of hydrogen was 
continually renewed from L, while the tap c controlled the admission of chlorine to 
the jet. The elongation of the chlorine flame showed when the atmosphere was 
failing, but the readings of the manometer P were chiefly relied on in following the 
changes of pressure of the hydrogen. 

During the combustion the endeavour was made so to regulate the admission of 
hydrogen as to keep it at a pressure just below atmospheric, but more often than not 
the attempt failed, owing to the rapid rate at which the gases burnt and the small 
size of the combustion vessel. If the flame went out, the hydrogen atmosphere had 
to be restored and the chlorine re-lit by a spark, but this seldom occurred during the 
experiments. 

The hydrogen chloride, immediately after its formation in the flame, was condensed 
as a pure white solid by the liquid air surrounding the lower end of the vertical limb 
B ; some chlorine, too, which had escaped burning in the flame, was condensed along 
with the hydrogen chloride. As the solid accumulated, the liquid-air vessel was 
gradually raised so that, at the end of the combustion, nearly the whole of B was 
immersed in liquid air. 

The combustion was continued until only a few grammes of liquid chlorine were 
left in E, when the tap / of the palladium bulb was finally closed and L allowed to 
cool. The flame was now made very small. As the atmosphere became rarefied, the 
flame became more and more attenuated until, just before it went out,*e was finally 
closed. The combustion, the average duration of which was over four hours, was then 
at an end. 

Then the residual gases in the vessel were sucked out by the pump through m, 
collected and subsequently analysed. The vapour pressures of solid hydrogen chloride 
and solid chlorine at the temperature of liquid air were so exceedingly small that 
none could be detected in the gases pumped out. In the gas analysis it was assumed 
that both these gases were absent. Even in the highest vacuum obtainable under 






DR. EDWARD C. EDGAR ON THE ATOMIC WEIGHT OF CHLORINE. 9 

the prevailing conditions, some hydrogen must still have adhered to the walls of the 
quartz vessel A ; but preliminary experiments showed the amount could not have 
been greater than 1 part in 55,000 of the hydrogen used. If a correction could be 
applied for this small weight of gas, it would have the effect of raising slightly the 
atomic weight of chlorine. 

The Sprengel pump fastened to m was now separated by fusion from the apparatus, 
and the tap p was closed so as to isolate the mercury in the manometer from 
subsequent contact with hydrogen chloride and chlorine. 

The next series of operations was to evaporate the snow-white hydrogen chloride in 
B and to condense it in the bomb immersed in liquid air. The successful accomplish- 
ment of this required very careful manipulation, the details of which were only learnt 
in the light of many failures. 

The first step was to warm gently the mercury in the quartz test tube Q so as to 
fill the chlorine condenser with mercury vapour. To prevent its diffusion into the 
bomb the coil R was surrounded by a freezing mixture of solid carbon dioxide and 
ether. The steel tube X was now partially immersed in liquid air ; the taps n and r 
and the screw valve W were opened ; and the evaporation of the solid hydrogen 
chloride was commenced by slowly lowering the- liquid air surrounding the limb B. 
The solid gradually evaporated into the combustion vessel, whence the gas passed on 
to the chlorine absorption apparatus. Here all traces of chlorine combined with 
mercury vapour and condensed as mercuric chloride. That the absorption of chlorine 
was complete was shown conclusively by the bright surface of mercury in the broad 
manometer tube T remaining untarnished at the end of the condensation. It was 
found, in preliminary experiments under similar conditions, that no weighable amount 
of mercury vapour could diffuse backwards out of Q. 

The purified hydrogen chloride, after its passage through Q, passed on to the steel 
tube X and there condensed. By repeated trials it was found possible so to lower the 
bomb into liquid air as to effect the condensation at a pressure never exceeding two- 
thirds of an atmosphere. 

The condensation took over four hours. When it was complete, the taps n and r 
and the screw valve W were closed ; and the whole apparatus was taken to pieces. 
Then the palladium bulb, the liquid chlorine bulb, the chlorine condenser, and the 
bomb were cleaned and weighed. 

In six experiments, then, the hydrogen chloride formed in the combustion was 
condensed in a steel bomb by liquid air. In two other experiments Y (fig. 7) was 
substituted for the bomb and the gas was condensed and weighed in water. In this 
case the manipulation varied a little from that adopted in condensing the gas by 
liquid air. Y was placed in a salt-ice mixture so as to freeze slowly the 100 c.c. of 
water it contained. This done, Y was attached to a pump and rapidly evacuated. 
At the end of the evacuation the phosphorus pentoxide showed no signs of harmful 
deliquescence. The taps z and y having been closed, Y was disconnected from the 

VOL. CCIX. A. C 



10 DR. EDWARD C. EDGAR ON THE ATOMIC WEIGHT OF CHLORINE. 

pump and weighed. It was then attached to the rest of the apparatus by a ground- 
glass joint. 

The evaporation of the solid hydrogen chloride in B and its passage through Q was 

conducted as before, though at a lower pressure. 

The purified hydrogen chloride passed through the taps z and y into the bulb Y, 
surrounded at first by cold water, later by a calcium-chloride-and-ice freezing 
mixture. Here the gas was absorbed; occasional shaking of Y kept down the 
pressure. Towards the end of the absorption, when only a very little solid hydrogen 
chloride was left in B (fig. 3), the tap y was closed and the end of the thick-walled 
capillary tube Z was immersed in liquid air. The last traces of hydrogen chloride 
condensed here. Preliminary experiments showed that in a high vacuum no 
measurable amount of hydrogen chloride could cling to the walls of the quartz 
combustion vessel. As an extra precaution, however, the walls of A were always 
warmed by hot water during the last stages of the condensation of hydrogen chloride. 

Z was separated by fusion from Y, but was afterwards weighed along with it. 
Finally, the different parts of the whole apparatus were disconnected as before. 

9. Analysis of Residual Gases. The analysis of the residual gases was carried out 

as follows : 

Fi" 1 . 8 is a sketch of the apparatus in which the gases were collected. It consisted 

of a graduated glass reservoir A furnished with two taps, B and C, and connected with 

a graduated tube I). The weight of the apparatus, filled with 
mercury between the taps B and C, having been determined, 
D was filled with mercury and the whole placed in a mercury 
trough. The gases were collected in D and passed into A ; 
it was assumed they were hydrogen and nitrogen. 

The gas apparatus, standing in the trough, was then taken 
to the balance room. The tap C was opened and the whole 
allowed to reach the temperature of the room. By noting 
the difference in level of the mercury in A and of the 
mercury in the trough, with the aid of the etched scales on 
A and D, the divisions of which were 1 mm. apart, and by 
subtracting this difference from the barometric height the 
pressure of the gases was found. The tap C was closed, the 
tube D emptied, and the gas apparatus was again weighed. 

The difference in the weights of the apparatus before and after the collection of the 

residual gases (corrected for the weight of these residual gases) gave their volume 

under the ascertained conditions of temperature and pressure. 

D having been refilled with mercury, the gas apparatus was replaced in the trough, 

C was opened, and successive small volumes of pure, dry oxygen added to the gases. 

Between each addition C was closed and the platinum spiral in A was cautiously heated 

by an electric current so as to bring about the combination without explosion of all 




Fig. 8. 



DK. EDWARD C. EDGAR ON THE ATOMIC WEIGHT OF CHLORINE. 



11 



the oxygen with the hydrogen. When the volume of oxygen added was just below 
half the volume of the residual gases, the tap C was temporarily closed. The gas 
apparatus, still standing in the trough, was then attached by the inner portion E of a 
ground-glass joint to a Sprengel pump. After the pump had been thoroughly 
evacuated, the tap B was opened and the small remaining volume of wet hydrogen 
and nitrogen (in no experiment exceeding 4 c.c. in volume) was sucked out of A. At 
the same time the tap C was cautiously opened so as to allow mercury to rise slowly 
in A and fill the whole apparatus, thus removing the last traces of gas from the 
apparatus. 

The wet nitrogen and hydrogen passed through a coil, immersed in a freezing 
mixture of solid carbon dioxide and ether. Most of the water vapour in the gases 
condensed in the coil. The dried gases then passed through the pump and were 
collected in another gas apparatus, a sketch of which is to be found on p. 193 of 
DIXON and EDGAR'S paper. The details of the subsequent gas analysis are given in 
full on the same page. 

The composition of the residual gases of the combustion, assuming they were 
hydrogen and nitrogen, was thus arrived at by subtracting from the total volume 
collected in the first gas apparatus (fig. 8) the volume of nitrogen found in the 
second. 

10. Results of the Experiments. In the tables set out below are given the results 
of eight experiments. Table II. contains the volumes of residual gases, in each 
experiment, reduced to normal temperature and pressure. 

TABLE II. Volumes of liesidual Gases (Cubic Centimetres at N.T.P.). 



Experiment . . I. II. III. IV. V. VI. 


VII. 


VIII. 


Volume of hydrogen 
unburnt 38-14 45-81 36-46 40-72 45-09 i 39-58 


43-17 


38-42 


Volume of nitrogen 
found ' 0-10 0-09 0-07 0-04 0-05 0-07 


0-02 


0-03 



In Table III. are placed the weights of chlorine which escaped burning in the flame 
and were caught by mercury in the chlorine absorption apparatus. 

TABLE III. The Weights of Chlorine Uncombiued with the Weighed Hydrogen 

(in Grammes). 



Experiment . . 


I. 


II. III. 


IV. 


V. 


VI. 


VII. 


VIII. 


Unburnt chlorine. . . 


0-0645 


I 

0-1338 0-1032 


0-0979 


0-0612 


0-1158 


0-0761 


0-1087 



c 2 



12 DR. EDWARD C. EDGAR ON THE ATOMIC WEIGHT OF CHLORINE. 

Table IV. gives the weights of the palladium bulb and the liquid chlorine bulb, in 
each experiment, before and after the combustion, together with the corrections for 
buoyancy and for the unburnt gases. The corrected weights of hydrogen chloride, 
caught in the steel bomb in Experiments 1, 2, and 4, and condensed in water in 
Experiments 7 and 8, are also given. In Experiments 3, 5, and 6 the individual 
weighings of the bomb were so discordant that it was obvious the screw valve 
had not been closed tightly enough, and that the bomb had been steadily leaking 
since its removal from the liquid air. 



DR. EDWARD C. EDGAR ON THE ATOMIC WEIGHT OF CHLORINE. 



13 



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[ 15 } 

II. On Scandium. 

By Sir WILLIAM CROOKKS, D.Sc., F.R.S. 

Received March 4, Read April 30, 1908.* 

[PLATE 1.] 

SOANDIA is one of the rarest and least known of the recognised rare earths. It was 
discovered in 1879 by NlLSON, who separated it, with ytterbia, from erbia extracted 
from euxenite and gadolinite. NILSON made an incomplete chemical examination 
of some of its compounds, but owing to the inadequate amount of material at his 
disposal he did not at first entirely separate it from ytterbia. Later in the same 
year CLEVE extracted scandia from gadolinite, yttrotitanite, and keilhauite, and 
described the scandium sulphate, double sulphates, nitrate, oxalate, double oxalates, 
selenate, acetate, formate, oxide, and hydrate, and gave some of the chief reactions of 
the new body. 

CLEVE, working on gadolinite, found that it contained only from 0'002 to O'OOB per 
cent. of scandium, while keilhauite yielded only about O'OOo per cent. He 
gave results from which he deduced an atomic weight of about 45. CLEVE noticed 
that scandium almost exactly corresponded to the description given by MENDELEEFF 
of his hypothetical element " ekaboron," of atomic weight 44. More recently, in 
1880, NILSOX, working on somewhat larger quantities of scandia, described and 
analysed the nitrate, sulphate, selenate, oxalate, and the potassium double sulphate. 
He found the atomic weight to be 44 '03, the mean of four separate and closely 
concordant determinations. Taking NILSON'S data, and re-calculating from them the 
atomic weight of scandium, using the most recent figures for oxygen and sulphur, 1 
find his atomic weight to be almost exactly 44'1 a figure I have used in the 

cj ./ O 

following paper. 

In the course of my 20 years' work on the fractionation of the rare earths I have 
repeatedly tested my products by examining their photographed spectra, using the 
dominant lines of the various elements as tests for their presence. Scandium has an 
extremely characteristic group of lines in its spectrum, situated between wave-length 
3535-864 and wave-length 365T983, the strongest being at 3613'984, midway 
between two strong iron lines. By using a part of the spectrum in which this 
line occupies the centre of the photograph, it is easy to recognise scandium. 
Detecting the dominant line, the presence of scandium can be verified by reference to 
the other lines of the group. (See the plate at the end of this paper.) 

* The descriptions and analyses of the Fluoride, Succinate, Benzoate, the Toluates, Phenyl-acetate, 
Pyromellitate, and Camphorate were received June 25, 1908. 

VOL. CCIX. A 442. 4.11.08 



1(3 SIE WILLIAM CKOOKES ON SCANDIUM. 

Scandium I found in some of my fractions, but only in small quantities. A few 

years ago I commenced an examination of all the obtainable rare-earth minerals, in 
order to see if any of them showed more than a trace of scandium. The minerals 
examined were : 

^Eschynite Homolite Thalenite 

Allanite Keilhauite Thorianite 

Alvite Knopite Thorite 

Auerlite Koppite Thorogummite 

Baddeleite (Ceylon) Lanthanite Tscheffkinite 

Bastnasite Monazite Tysonite 

Broggerite Mosandrite Urdite 

Cerite Orangite Wiikite 

Cleveite Orthite Xenotime 

Columbite Polycrase Yttergarnet 

Cryptolite Pyrochlore Yttrialite 

Eudialite Rhabdophaiie Yttrocerite 

Euxenite Samarskite Yttrogummite 

Fergusonito (Ceylon) Scheelite (Bohemia) Yttrotantalite 

Fergusonite (Ytterby) Scheelite (New Zealand) Yttrotitanite 

Fluocerite Schorlomite Zirkelite (Ceylon, sp. gr. 5'0) 

Gadolinite Sipylite Zirkelite (Ceylon, sp. gr. 4-42) 

Hielmite Tantalite 

Of these minerals scandium was detected in auerlite, cerite, cryptolite, keilhauite, 
koppite, mosaiidrite, orangite, orthite, pyrochlore, thorianite, thorite, urdite, and 
wiikite. But while the other minerals contained less than O'Ol per cent, of scandium, 
wiikite was found to contain more than one hundred times that amount. 

Wiikite is a black amorphous mineral found with monazite in a felspar quarry at 
Impilaks, Lake Ladoga, Finland. It is named after Professor WllK, of Helsingfors 
(' Min. Mag.,' vol. xiii., p. 379). 

I have compared wiikite with a large number of typical rare-earth minerals, and in 
appearance I find it most resembles yttrotantalite. A thin section under the microscope 
looks like solidified mud. It is quite amorphous, breaks with a conchoidal fracture, 
shows no crystalline structure, and has no action on polarised light. 

Wiikite is somewhat radio-active. A fragment was laid on a sheet of 
sensitive film opaque black paper intervening for ninety-five hours. Subsequent 
development revealed a good impression, about equal in strength to what would be 
given by pitchblende in twenty-four hours. The image was not uniform, and at one 
point radiation had spread from the mineral over the adjacent part of the sensitive 
film. 

The specific gravity of wiikite is 4 '85. Its hardness is 6. It is infusible before the 
blowpipe. It is imperfectly attacked by strong mineral acids and breaks up easily 
when fused with potassium bisulphate. Heated to full redness in a silica tube it 
gives off helium, water, and a distinct amount of sulphuretted hydrogen, followed by 



SIR WILLIAM CKOOKES ON SCANDIUM. 17 

a white sublimate. The mineral begins to crack at a temperature a little below 
redness, and, at the approach of redness, gas is evolved with almost explosive violence, 
the mineral breaking and flying about the tube. A fragment so treated examined 
under the microscope shows a surface covered with glistening points. With a high 
power these points are resolved into a mass of minute cubes, curiously regular in form 
and appearance. Heating drives off 5 '8 3 per cent, of its weight ; 5 "8 2 of the loss is 
water and acid vapour, the difference, O'Ol per cent., consists chiefly of helium, with 
a little hydrogen, carbon dioxide, and a mere trace of neon. The average amount of 
gas collected from 100 grs. of the mineral was 15 '6 cc. Sir JAMES DKWAR kindly 
passed the gases for me over hot oxide of copper and then through charcoal immersed 
in liquid air. This should absorb and retain everything but helium and the trace of 
neon. The eas thus purified, after exhaustion to the most luminous point, was sealed 
in a double-bulb silica tube. The spectrum, visual and photographed, was that of 
pure helium with a scarcely perceptible trace of neon. 

Containing so many bodies, the exact separation of which one from the other is not 
known, it is at present impossible to give an accurate and complete analysis of 
wiikite. Moreover, I find the composition varies somewhat in different samples of the 
mineral. The following is considered a fair approximation of the composition of a 
typical specimen : 

Tantalic acid with some niobic acid 1 5 '9 1 

Titanic acid and zirconia 23 '36 

Earths of the cerium group 2 '5 5 

Earths of the yttrium group 7 '6 4 

Scandia 1-17 

Thoria 5 '51 

Ferrous oxide 15 '52 

Uranic oxide 3 '56 

Silica 16'98 

Water and gases 5 - 83 

Calcium, manganese, tin, sulphur, &c., unestimated . . 1'97 

100-00 

The percentage of scandia is too low. Owing to the difficulty of separating it 
completely from the accompanying earths and metallic acids, the amount given is 
only that which has been obtained in an approximately pure state. 

I find the following the best process to extract scandia from wiikite : The 
ground mineral is passed through an 80-mesh sieve, then mixed with five times its 
weight of powdered potassium bisulphate and fused in a clay crucible. At first much 
frothing occurs, due to the escape of permanent gases and aqueous vapour ; this 
ebullition can be abated by stirring with an iron rod. When in quiet fusion, the heat 
is raised to full redness for ten minutes and the liquid mass poured on an iron plate. 

VOL. CCIX. A. D 



18 SIE WILLIAM CROOKES ON SCANDIUM. 

When cold, the melt is finely ground, mixed with water in the proportion of 1 kilo, 
to 5 litres, and mechanically agitated for about twelve hours. It is then thrown on 
a linen filter and well washed. This treatment extracts most of the rare earths, 
together with a little titanic, iiiobic, and tantalic acids and zirconia, but the bulk of 
these bodies is left behind. 

The solution is supersaturated with ammonia and well boiled ; this treatment 
precipitates all the earths, together with iron, titanic acid, zirconia, &c. The 
precipitate of crude earths is filtered and well washed. 

The precipitated crude earths are converted into oxalates by heating the pasty 
precipitate in a dish with crystals of oxalic acid added gradually, excess being avoided 
as much as possible. When cold, the oxalates are filtered off, and the iron, &c., in 
the filtrate is precipitated with ammonia. As scandium oxalate is slightly soluble in 
water, the iron precipitate will contain a certain proportion, which must fee kept for 
subsequent working up. 

The washed oxalates are dried and ignited ; the resulting earths form about 
17 per cent, of the mineral and contain about 7 per cent, of scandia. 

The crude oxides are converted into sulphates by heating with sulphuric acid, the 
excess of acid being driven off by heat -not using too high a temperature. The dry 
sulphates are agitated with plenty of water, and filtered from a little insoluble residue 
of metallic acids. Ammonia in excess is then added to the filtrate, and the precipitated 
oxides are washed, once more converted into oxalates in the manner already described, 
and the oxalates again washed, dried, and ignited. The ignited oxides are boiled in 
dilute nitric acid, filtered from a little insoluble matter, and evaporated to dryness. 
These somewhat complicated operations are to insure the removal of sulphuric and 
metallic acids, the presence of which interferes with subsequent fractionation. 

The earthy nitrates rich in scandium are mixed with an equal bulk of potassium 
nitrate and fused in large porcelain crucibles with constant stirring until the mass has 
the appearance of cream fluid when hot, solidifying on cooling to a white enamel-like 
mass. On boiling this mass in water, a dense white basic nitrate separates and 
undecomposed nitrates are left in solution. Scandium and ytterbium, forming easily 
decomposed nitrates, concentrate in the insoluble end the " heads," while the 
yttrium and cerium earths, whose nitrates are less easily decomposed by heat, are left 
in the soluble end the "tails." Fractionation on these lines must now be continued 
until spectrum photographs show the scandium to be pure. It is not difficult to obtain 
scandia free from all earths present except ytterbia and yttria ; but the final elimination 
of pure scandia from these earths is a matter demanding much time and patience. 

This easy decomposition of the nitrate by heat makes it possible by a systematic series 
of fractionations to separate scandium from most of the other associated elements. 
The worst impurity is ytterbium, the nitrate of which is almost as easily decomposed. 
Fortunately a strong dominant line of the ytterbium spectrum, wave-length 3694'344, 
occurs at a vacant part of the scandium spectrum, and near the characteristic group 






SIE WILLIAM CROOKES ON SCANDIUM. 19 

of scandium. A sample of scandia is not considered satisfactory if the least trace 
of this line is seen on an over-exposed spectrum of scandium, and if the atomic weight 
is higher than 44'1. The atomic weight of ytterbium being 173, a very little of it as 
an impurity raises the atomic weight of scandium. 



SCANDIUM HYDROXIDE, 
Sc 2 3 ,3H 2 = Sc(OH) 3 . 

On adding caustic alkali to a solution of a scandium salt the hydroxide comes 
down as a bulky gelatinous precipitate. It is insoluble in excess of precipitant. In 
appearance it resembles yttrium hydroxide. It dries in the air at ordinary tempera- 
tures to a hard porcelain-like mass and has the composition given above. 

Analysis. 

5 '289 grs. lost on ignition 1'533 grs. of water. 

Theory. Experiment. 



Sc 2 O 3 .... 136-200 7T59 71'02 

3H 2 O 54-048 28 "41 28'98 



190-248 100-00 100-00 

The hydroxide is a very weak base, with a marked tendency to form basic salts. 
It dissolves readily in dilute acids, forming salts which have a sweet astringent taste. 
The salts show no absorption spectra. 

After ignition, anhydrous scandia, Sc 2 O 3 , is difficultly soluble in dilute acids in the 
cold, rather more easily soluble when warmed, and readily soluble in hot strong 
mineral acids. Strong sulphuric acid poured on ignited scandia attacks it with 
considerable evolution of heat. ^ 



SCANDIUM CARBONATE, 
Sc 2 (C0 3 ) 3 ,12H 2 0, 

comes down as a bulky white precipitate on adding ammonium or sodium cai'bonate to 
a soluble salt of scandium. It is almost insoluble in a cold dilute solution of ammonium 
carbonate, but is moderately soluble in a hot and strong solution of this salt, and as 
in the same circumstances yttrium carbonate is much less soluble, this difference 
may be utilised as a basis for a method of separating scandium and yttrium by 
fractionation. 

D 2 



20 SIR WILLIAM CROOKES ON SCANDIUM. 

Scandium carbonate holds carbonic acid very weakly, and concordant analyses are 
not easy to get. Drying at 100 drives off water and some of the carbon dioxide, 
leaving a basic carbonate. When freshly precipitated and dried in a current of air 
at the ordinary temperature, the following formula best agrees with the figures 

obtained : 

Sc 2 (C0 3 ) 3 ,12H 2 0. 

At a temperature of 100 this salt loses carbon dioxide and water, and becomes a 
basic salt of uncertain composition. 

Strong ignition drives off all water and carbon dioxide, leaving Sc 2 3 . 

HYDRATED SCANDIUM CHLORIDE, 

Sc 2 CU2H 2 O. 

The hydrated salt is prepared by dissolving the earth in hydrochloric acid and 
evaporating on a water-bath. It crystallises from a strong solution as a felt-like mass 
of fine white needles. The crystals should be pressed many times between filter-paper 
frequently renewed, and put to dry for a few hours in a desiccator over sulphuric 
acid. They are somewhat deliquescent, but not so much so as the nitrate, and are 
readily soluble in alcohol. They have the following composition : 

Sc 2 01 6 ,12H 2 = Sc 2 3 ,GHCl,9H 2 0. 

Analysis. 

(1) G'087 grs. of the pressed chloride left on ignition T620 grs. of scandia. 
("2} 5'9GO grs. of the pressed chloride lost T83G grs. after remaining in the water- 
oven at 100 for six hours. 

Theory. Experiment. 







(1) and (2). 


136-200 


26-34 


26-61 


218748 


42-30 


42-58 


162-144 


31-36 


30-81 



Sc 2 3 .... 
GHC1 .... 
9H 2 O .... 

517-092 100-00 100-00 

When heated for six hours to a temperature of 100, the 9 molecules of water go 
off, leaving a clear, colourless, and oily liquid, which on cooling solidifies to a white 
crystalline mass of the composition . 

Sc a Cl 6 ,3H 3 = Sc 2 3 ,6HCl. 

When this salt is gradually heated to redness it gives off 6 molecules of hydrochloric 
acid with much intumescence, leaving a bulky residue of scandia. 



SIR WILLIAM CROOKES ON SCANDIUM. 21 

Analysis. 

(1) 4*235 grs. on ignition left 1*620 grs. of scandia, = T049 grs. of scandium. 

(2) 4'124 grs. were dissolved in water and the scandia precipitated by ammonia. 

The scandia obtained weighed 1*592 grs., = 1*031 grs. of scandium. 

Theory. Experiment. 

(1). (2). ' 

2477 25-00 

75-23 75-00 



2Sc. . . 


88*200 


24*85 


601. . . 


. ] 




3H 2 O . . 


^266*748 


75*15 



354-948 100-00 lOO'OO lOO'OO 

HYDRATED SCANDIUM BROMIDE, 
Sc 2 Br 6 ,12H 2 0. 

Scandium hydroxide or carbonate dissolves easily in hydrobromic acid, and the acid 
solution evaporated on the water-bath deposits small rhombic crystals, coloured 
slightly brown by free bromine and very deliquescent. These crystals were collected 
on filter-paper and dried by pressure between folds of paper frequently renewed. 
They were then put into a silica weighing bottle, and dried in a desiccator over 
sulphuric acid. 

Analysis. 

(1) 29-753 grs. of the hydrated bromide gave on ignition 5'068 grs. of scandia. 

(2) 29-753 grs. of the hydrated bromide lost at 120 6'207 grs. of water. 





Theory. 




Experiment. 


f 






(1) and (2). 


Sc 2 3 . . 


. . 136-200 


17-37 


17-03 


6HBr . . . 


. 485-808 


61-95 


62-11 


9H 2 . . . 


. 162-144 


20-68 


20-86 



784-152 100-00 lOO'OO 

When the hydrated bromide is heated in an air-bath to 120 it loses 9 molecules of 

water and becomes 

Sc 2 Br e ,3H 2 = ScA,6HBr. 

Analysis. 

23'546 grs. of the dried bromide left on ignition 5'068 grs. of scandia. 

Theory. Experiment. 



ScA . 
GHBr . 


. . . 136-200 

. . . 485-808 


21-89 
78-11 


21-53 

78-47 



622-008 100-00 lOO'OO 



22 SIR WILLIAM CROOKES ON SCANDIUM. 

SCANDIUM FLUORIDE, 

Sc 2 F 6 . 

Ignited scandia is attacked by aqueous hydrofluoric acid, forming a semi-transparent 
gum-like mass, which on boiling changes to a fine white precipitate. This is difficult 
to filter, as it has great tendency to run through. 

When hydrofluoric acid is added to a solution of scandium nitrate or sulphate, a 
white precipitate comes down. On boiling it becomes milky, resembling the above- 
described precipitate. 

The. fluoride dried over sulphuric acid is anhydrous. It slightly loses weight at a 
red heat, and at a yellow heat it frits together, fusing with difficulty before the 
blowpipe. 

Strong sulphuric acid imperfectly decomposes scandium fluoride. It is completely 
decomposed by fusion with potassium bisulphate. ; the melt dissolves in acidulated 
water, and the solution mixed with ammonia deposits scandium hydroxide. 

Analysis. 

8'!). r )f> grs. of scandium fluoride, decomposed by fusion with potassnun bisulphate 
and precipitated by ammonia, gave 0-0305 grs. of scandia, = 3'9091 grs. of 
scandium. 

Theory. Experiment. 



So, 88-2 43-02 43'G5 

F K .... 114-0 50-38 56-35 



202-2 I ()()()() 100-00 

SCANDIUM CHLORATE. 

Aqueous chloric acid saturated with scandium hydroxide forms at first a clear 
colourless liquid; evaporation on the water-bath decomposes it, with evolution of 
chlorine. On further evaporation, crystals like long needles form on cooling, 
and the mother-liquor becomes a gummy amorphous mass in which, after standing, 
appear long needle-shaped crystals. These crystals probably are the perchlorate. 

SCANDIUM PERCHLORATE. 

Aqueous perchloric acid easily dissolves scandium hydroxide or carbonate, and the 
solution evaporated over the water-bath separates into a felt-like mass of rhombic 
needle-shaped crystals. 



SIR WILLIAM CROOKES ON SCANDIUM. 23 

SCANDIUM BROMATE. 

Bromic acid readily dissolves scandium hydroxide, but on evaporating the solution 
it decomposes, leaving an amorphous gummy mass without crystalline appearance. 

SCANDIUM SULPHATE, 

Sc 2 (SO 4 ) 3 ,GH 2 O. 

Scandium hydroxide easily dissolves in dilute sulphuric acid ; after ignition the 
oxide dissolves with difficulty in dilute, but readily in strong acid, with evolution of 
heat. The excess of sulphuric acid must he driven off carefully, when the anhydrous 
sulphate is left behind in the form of a fine white powder. 

NlLSON gives the formula of the anhydrous salt, Sc 2 O tf ,3S() a . He says : " It loses 
acid at a high temperature, and leaves pure scandia. The salt treated with water 
only gives at first a milky liquid, the anhydrous salt combines very slowly with water, 
and then re-dissolves. On heating, a clear solution is immediately obtained." 
According to CLEVE, " Sulphuric acid gives with scandia a white and bulky mass of 
sulphate, resembling thorium sulphate when it separates by heat. The sulphate does 
not form distinct crystals." It is very soluble in water, and a strong solution when 
heated does not deposit crystals, in that respect differing from most of the other rare- 
earth sulphates. The solution may be evaporated to a super-saturated syrup, which, 
standing in the cold for some hours, deposits crystals of the G-hydrate. TOO parts of 
the saturated solution at 12 were found to contain 44 '5 parts of anhydrous scandium 
sulphate. Scandium sulphate is not deliquescent in the ordinary air of a room even 
in damp weather, and is insoluble in alcohol. On mixing 100 grs. of anhydrous 
scandium sulphate with the same quantity of water, the temperature rose in a few 
minutes from 14 to 21. 

On adding absolute alcohol to a strong solution of scandium sulphate the solution 
becomes milky, and a heavy oily-looking liquid sinks to the bottom. This may be 
separated by filtration through paper moistened with alcohol, when the residue is left 
as a viscous liquid which on exposure to the air becomes thicker. This oily-looking 
liquid has the composition of the 6-hydrate sulphate. 

When strongly heated, the sulphate decomposes, leaving pure scandia. It is, how- 
ever, difficult to drive off all the sulphuric acid from the sulphate even by heating the 
crucible containing it before the blowpipe. The best way to decompose scandium 
sulphate is first to ignite it to the highest temperature of a Bunsen burner, then to 
moisten with water and add a little ammonium carbonate. Dry and ignite again, and 
pure scandia is left free from sulphuric acid. 

NILSON says : " This salt separates from a syrupy solution in small globular 
aggregates. It is inalterable in the air, it loses four molecules of water at 100, 



24 SIR WILLIAM CROOKES ON SCANDIUM. 

and the rest at a higher temperature." He found on analysis 14'26, 14'46, and 7'16, 
7'29 of H 2 0, instead of 14'88 and 7'44. 

I have crystallised this sulphate from a syrupy aqueous solution ; it is dried by 
repeated pressure between many folds of blotting-paper. 

Analysis. 

(1) 18'15G grs. of the crystallised G-hydrate, finely powdered, and heated to 100 

for three hours, lost 2 '602 grs. of water, leaving a 2-hydrated sulphate. 

(2) 20725 grs., kept in a desiccator over sulphuric acid for 170 hours, lost 1'561 

grs. of water, leaving a 4-hydrated sulphate. 

(3) 29'138 grs. left on ignition 8'068 grs. ofscandia. 

(4) 31 '508 grs. of the liquid sulphate, precipitated from solution on adding alcohol 

containing a little ether, were dissolved in water, and the scandia precipitated 
by ammonia. When dried and ignited it weighed 8 '624 grs. 

Theory. Experiment. 

(1), (2), (3), and (4). 
Sc 2 3 .... 136-200 28-11 27-53 

3SO 3 240-180 49-58 50'61 

2H 3 .... 36-032 7-44 7 "53 

4H 2 . . . 72-064 14-87 14-33 



484-476 100-00 lOO'OO 

The 6-hydrate effloresces in a dry atmosphere, and loses one molecule of water, 
becoming the 5 -hydrate, which appears to be the most stable hydrate at ordinary 
temperatures : 

Sc 2 (S0 4 ) 3 ,5H 2 0. 



Analysis. 

(1) 16'619 grs. of the 5-hydrate, heated to 150, lost 3'206 grs. of water. 

(2) 16-619 grs., after drying as described and igniting to a yellow heat, left 

4 - 8 7 8 grs. ofscandia. 

(3) 15-608 grs. of the 5-hydrate, heated in vacua at 100 for twenty hours, and 

then for ninety minutes at 150, lost 3 '15 3 grs. of water. Ignited to a full 
yellow heat, it left 4 '5 5 8 grs. ofscandia. 

(4) 38-819 grs., heated to just below visible redness, lost 8'019 grs. of water. 

(At this temperature a trace of basic sulphate is formed. This accounts 
for the excess over the theoretical loss of water.) 



SIR WILLIAM CROOKES ON SCANDIUM. 25 

Theory. Experiment. 









(1). 


(2). 


(3). 


(4). 


ivieau. 


Sc 2 O 3 . . 


. 136-20 


29-20 


- 


29-35 


29-20 





29-27 


3SO 3 . . 


, 240-18 


51-49 














50-68 


5H 2 O . . , 


90-08 


19-31 


19-29 





20-20 


20-66 


20-05 



466-46 100-00 lOO'OO 

ANHYDROUS SCANDIUM SULPHATE, 
Sc 2 (S0 4 ).,. 

When the hydrated sulphate is heated to 250 it loses the whole of the water and 
becomes anhydrous. Its composition now is Sc 2 (SO,) a . 
At a bright yellow heat all the sulphuric acid goes off. 

Analysis. 

(1) 30-716 grs. left on ignition Ll'092 grs. of scandia. 

(2) 18-907 grs. left on ignition 6'827 grs. of scandia. 

Synthesis. 

(3) C'817 grs. of ignited scandia, converted into sulphate, yielded 18 '907 grs. of 

scandium sulphate. 

Theory. Experiment. 









(1). 


(2). 


(3). 


Sc 8 3 


. . . 136-20 


36-19 


3(5-11 


36-11 


36-06 


3SO 3 


. . . 240-18 


63-81 


63-89 


63-89 


63-94 



376-38 100-00 lOO'OO lOO'OO lOO'OO 

When the anhydrous sulphate is heated to dull redness it loses one molecule of 
SO 3 , and becomes a basic salt of the composition 

Sc 2 0(SO,) 2 . 

Synthesis. 

4'622 grs. of ignited scandia were dissolved in strong sulphuric acid, the excess 
of acid driven off by heat, and the dry sulphate heated to dull redness-. It 

weighed 10 '121 grs. 

Theory. Experiment. 



Sc 2 O 3 136-20 45-97 45"67 

2S0 3 160-12 54-03 54'33 

g __ _^___^__ 

296-32 100-00 100'OQ 
VOL. CCIX. A. E 



26 SIR WILLIAM CROOKES ON SCANDIUM. 

SCANDIUM AND POTASSIUM DOUBLE SULPHATE, 
3K 2 S0 4 ,Sc 3 (S0 4 ) 3 . 

The behaviour of the double sulphates of potassium and the rare-earth metals is 
usually considered to govern their position in the broad groups into which they are 
divided. If the double sulphate is insoluble in a saturated solution of potassium 
sulphate the earth is supposed to belong to the cerium group, while if the double 
sulphate is soluble the earth is said to be one of the yttrium group. According to 
CLBVE (' Comptes Rendus,' vol. Ixxxix., p. 419, August 18, 1879): "Potassium 
sulphate in concentrated solution gives rise to the separation of a double salt, a 
crystalline powder, soluble in a saturated solution of potassium sulphate." CLEVE 
gives the composition of the double salt as Sc 2 O 3 ,3SO 3 +2K 2 O,SO 3 . On the other 
hand, NlLSON says (' Comptes Rendus,' vol. xci., p. 118, July 12, 1880) : " Scandium 
sulphate in a saturated solution of potassium sulphate gives a double salt, completely 
insoluble. ... It dissolves with difficulty in water, even boiling, and not at all 
in a saturated solution of potassium sulphate. . . . The composition of the double 
salt, 3K 2 2 SO 2 + Sc 2 3SO a , shows that scandium belongs to the group of gadolinite 
and cerite metals, all these metals giving salts of the same typical composition." 

In .view of these diametrically opposite statements I have taken especial pains to 
ascertain the true behaviour 1 of the double salt. 

17 '7 17 grs. of re-crystallised scandium sulphate, found by analysis to be pure, were 
dissolved in water in a flask. The calculated quantity of potassium sulphate to unite 
with the 17'717 grs., and to make a saturated solution in the water added, was then 
weighed out, and 5 per cent, additional potassium sulphate was added to ensure 
complete saturation. This was dissolved in boiling water, put into the flask con- 
taining the scandium sulphate, and water up to 250 cc. was added. The flask was 
securely corked, and put into a mechanical agitator, where it was shaken continuously 
for twenty-five hours. At first, when the two salts were mixed, no precipitation 
of double salt was visible, but after a short time there appeared a fine granular 
precipitate, which gradually increased as the shaking proceeded. 

At the end of twenty-five hours the precipitated double sulphate was filtered 
off and washed with 100 cc. of cold saturated solution of potassium sulphate. The 
filtrate was heated, ammonia added, and the whole well boiled. A very slight 
precipitate of scandia came down which, when filtered, washed, and ignited, weighed 
0-414 gr., equivalent to T473 grs. of scandium sulphate in solution, the rest of the 
sulphate being in the insoluble precipitate. It therefore follows that for every 
100 parts of the double sulphate 8'32 per cent, are soluble and 91'68 per cent, are 
insoluble in the amount of saturated solution of potassium sulphate employed. 

The insoluble double salt was washed with boiling water to remove the little excess 
of potassium sulphate, until its bulk was reduced about one-half. It was then dried 
and analysed. 






SIR WILLIAM CROOKES ON SCANDIUM. 27 

My own analytical results agree closely with NILSON'S formula. As CLEVE distinctly 
says that the double sulphate is soluble in a saturated solution of potassium sulphate, 
it is probable he was not working on the true double salt. 

The scandia in the aqueous washings was also determined. The total amount of 
scaiidia in the washings and precipitate amounted to 4'560 grs., which, added to the 
0'414 in the solution, makes 4 '974 grs. of scandia. The 17717 grs. of scandium 
sulphate contain theoretically 4 - 981 grs. of scandia, so these results are well within 
experimental errors. 

SCANDIUM SELENATE, 
Sc 2 (Se0 4 ) 3) 8H 2 0. 

Dilute and warm selenic acid easily dissolves scandium hydrate or carbonate, and 
on evaporating the acid solution over sulphuric acid the selenate crystallises in well- 
defined rhombic prisms, bright, colourless, and capable of withstanding a temperature 
of 400 without decomposition, except loss of water. 

When heated to 100 for sixteen hours, the 8-hydrate loses 6 molecules of water 

and becomes a 2-hydrate, 

Sc 8 (Se0 4 ) 3 ,2H 8 O. 

Analysis. 

(1) 16 '847 grs. of crystallised scandium selenate, heated to 400, lost 3709 grs. of 

water. 

(2) 16'847 grs. of the same salt gave on ignition to a full yellow heat 3'485 grs. of 

scandia, = 2'257 grs. of scandium. 

(3) 13'913 grs. of the crystallised salt, heated to 100 for sixteen hours, lost 

2 '2 9 3 grs. of water. 

Theory. Experiment. 









(1), (2). 


(3). 


Sc 2 . . . 


88-200 


13-33 


13-39 





3Se0 4 . . 


. 429-600 


64-90 


64-60 





6H 2 O . 


. . 108-096 


16-331 21 . 77 


22-01 1 


16-48 


2H 2 . 


. . 36-032 


5-44 J 








661-928 100-00 lOO'OO 

The anhydrous selenate, heated to a full yellow heat, loses all the selenic acid, and 

scandia remains. 

Analysis. 

13-138 grs. of anhydrous seleiiate left 3'485 grs. of scandia, = 2'257 grs. of 
scandium. 

E 2 



28 



SIB WILLIAM CEOOKES ON SCANDIUM. 

Theory. Experiment. 



Sc 2 . 
3SeO, 




517-8 



17-03 
82-97 

100-00 



17-18 

82-82 

100-00 



SCANDIUM NITRATE, 

Sc(N0 3 ) 3 ,4H 2 0. 

When hydrated, scandia easily dissolves in dilute nitric acid ; after ignition it 
dissolves with the aid of heat in moderately strong nitric acid. The salt is very 
soluble in water and in alcohol, and is extremely deliquescent. The acid solution, 
over sulphuric acid, dries up to a viscous gummy mass, in which appear groups of 
stellate crystals. A neutral aqueous solution evaporated on the water-bath, on cooling, 
deposits colourless prismatic crystals. 

Scandium nitrate decomposes more easily by heat than the nitrate of any other of 
the rare earths. The crystals deposited from an almost neutral solution get pasty at 
100, but do not run to liquid. In vacuum at 100 the crystals give off water, and frit 
together, but do not become liquid. Dried on a water-bath, and heated in a tube 
immersed in melted paraffin with a thermometer by its side, they show signs of 
melting at 125. They commence to liquefy at 150, and when stirred with a platinum 
wire the crystals run together and form an opaque white liquid. 

When scandium nitrate is partly decomposed by heat, and the melted mass extracted 
with hot water and well boiled, a basic nitrate then deposits, which is difficult to filter 
owing to its clogging fineness. 

The hydrated nitrate, gradually heated in a silica crucible, fuses and boils, becomes 
opaque and evolves much water. If the heating is stopped at the proper time, the 
anhydrous nitrate is left, the whole of the water having been driven off. On 
continuing the heat nitrous vapours come off and the liquid becomes clear and liquid 
like w^ater. Increasing the heat turns the liquid brown and drives off more nitrous 
vapours, ebullition becomes sluggish, the fused mass gets white and opaque, and 
finally there remains a white residue of scandia. 

For analysis the nitrate was thrice re-crystallised and repeatedly dried between 
blotting-paper. 

Analysis. 

(1) 11-136 grs., gradually heated to full redness, left 2'537 grs. of scandia, 

= 1'6429 grs. of scandium. 

(2) 25-978 grs. left 5'914 grs. of scandia, = 3'8297 grs. of scandium. 



SIR WILLIAM CKOOKES ON SCANDIUM. 29 

Theory. Experiment. 



Sc. . . 
3(N0 3 ) . 
4H 2 . . 


. . 44-100 

'| 258-094 


14-59 
85-41 



0). (2). 

1475 14-74 

85-25 85-26 



302-194 100-00 100-00 lOO'OO 

When the above hydrate is dried over a water-bath, it does not fuse, but becomes 
pasty and anhydrous 

Sc(N0 3 ).,. 

Analysis, 

(1) 38795 grs. left on ignition 11'449 grs. of scandia, = 7'4141 grs. of scandium. 

(2) H'026 grs. of nitrate left on ignition 3'233 grs. of scandia, = 2'0936 grs. of 

scandium. 

(3) 14-618 grs. of nitrate left on ignition 4'287 grs. of scandia, = 27762 grs. of 

scandium. 

Synthesis. 

(4) 4'246 grs. of ignited scandia (= 27496 grs. of scandium) were covered in a 

crucible with strong nitric acid and put into a hot oven at 100 for seven 
hours. All excess of nitric acid disappeared, and a clear oily liquid 
remained which solidified on cooling. No crystals were seen, but the 
substance resembled glass. The solid nitrate weighed 14 '008 grs. 

(5) 3'233 grs. of scandia (= 2'0936 grs. of scandium), treated as described in the 

last experiment, formed 11 "026 grs. of nitrate. 

Theory. Experiment. 









(1). 


(2)- 


(3). 


(4). 


(5). 


Sc . . 


44-10 


19-16 


19-11 


18-99 


18-99 


19-63 


18-99 


3(N0 3 ) . 


186-03 


80-84 


80-89 


81-01 


81-01 


80-37 


81-01 



230-13 100-00 100-00 lOO'OO lOO'OO lOO'OO lOO'OO 

When the hydrated nitrate is dried in vacuo at 100 for seventeen hours it becomes 

a basic nitrate 

ScOH(N0 3 ) 2 ,H 2 0. 

Analysis. 
21-679 grs. of this basic nitrate lost on ignition 14'475 grs., and left 7 '2 04 grs. of 



scandia, = 4'665 grs. of scandium. 



30 



SIR WILLIAM CROOKES ON SCANDIUM. 

Theory. Experiment. 



Sc . . . . 


44-100 


2171 


21-52 


OH ... 


'] 






(N0 3 ) 2 . . . 


. M59-044 


78-29 


78-48 


H 2 0. . . . 


J 







203-144 



lOO'OO 



lOO'OO 



Therefore the nitrate has lost one equivalent of nitric acid. 

When the nitrate is heated for twelve hours in a hot-air oven at a temperature of 
120, a basic nitrate is left of the composition 

Sc 2 O(NO 3 ) 4 . 



Analysis. 

(1) G'550 grs. left on ignition 2'537 grs. of scandia, = l'G429 grs. of scandium. 

(2) 13'698 grs. left on ignition 5'287 grs. of scandia, = 3'4237 grs. of scandium. 



Theory. 



352-24 



100-00 



Experiment. 



2Sc 


. . 88-20 


25-04 


(1). 
25-08 


(2). 
24-99 


o . . . 


.1 








4(NO a ) . 


^264-04 


74-96 


74-92 


75-01 



100-00 



100-00 



SCANDIUM FORMATE, 
(HCOO) 2 ScOH,H 2 O. 

Scandium hydroxide dissolves readily in formic acid. The solution is evaporated to 
expel excess of acid and dissolved in water. It is then allowed to evaporate over 
sulphuric acid in a desiccator, when it forms hard and lustrous crystals, easily soluble 
in hot water and in alcohol. 

The formate readily decomposes when heated, and at a red heat leaves a white 
residue of scandia. 

Analysis. 

8'895 grs. of crystallised formate left on ignition 3'650 grs. of scandia, 
= 2'3G3 grs. of scandium. 



SIR WILLIAM CROOKES ON SCANDIUM. 31 

Theory. Experiment. 



Sc 44-10 26-07 26-57 

(HCOO) 2 . . . 

OH ^125-04 73-93 73'43 

H 2 O 



169-14 100-00 100-00 

SCANDIUM ACETATE, 
,211,0. 



Scandium oxide after ignition does not dissolve in acetic acid. The hydroxide, 
however, dissolves easily, and the acetate soon separates from the liquid in the form 
of fine white crystals, difficultly soluble in water. The aqueous solution, evaporated 
over the water-bath, deposits hard crystalline crusts. 

When freshly prepared, the acetate dried in the air has the composition given 
below. Water, however, is slowly given off, and after standing some days the salt 
passes into a monohydrate analogous to the formate. 

When ignited, the acetate leaves a grey residue of scandia containing carbon. By 
ignition alone it is difficult to get it of a constant weight. The best way to analyse 
the salt is to moisten the weighed acetate with a few drops of nitric acid and 
cautiously to evaporate to dryness, heat, and ignite. In this way is obtained pure 
white scandia. 

Analysis. 

(1) 7'795 grs. of acetate left 2'449 grs. of scandia, = 1'5859 grs. of scandium. 

(2) 7-133 grs. left 2'270 grs. of scandia, = 1-4097 grs. of scandium. 

(3) 19"035 gi's. left on ignition G'OOO grs. of scandia, = 3 - 8848 grs. of scandium. 

Theory. Experiment. 



(1). (-2). (3). 

Sc 44-100 20-49 20'35 20'00 20'41 

(CH 3 COO) 2 . . 

OH )>171-088 79-51 79-05 79'40 79'59 

2H 2 



215-188 100-00 100-00 lOO'OO lOO'OO 

After being exposed to dry air for several days, the dihydrate loses one molecule of 
water of crystallisation, and becomes a monohydrate 

(CH 3 COO) 3 ScOH,H 2 0. 



32 SIR WILLIAM CROOKES ON SCANDIUM. 

Analysis. 

14-690 grs. left 5 '262 grs. of scandia, = 3'4075 grs. of scandium. 

Theory. Experiment. 



Sc ... 44-100 22-37 23'19 

(CH 3 COO) 2 .. .' 

OH )>153'072 77-63 76'81 

H 2 0. 



197-172 100-00 100-00 

SCANDIUM PROPIONATE, 
(C s H 5 COO) 2 ScOH. 

Propionic acid readily attacks scandium hydroxide, forming a difficultly soluble 
white amorphous salt. On evaporating the excess of acid the scandium propioriate is 
left as a voluminous white powder. 100 parts of cold water dissolve 1"23 parts of 
scandium propionate, the greater part being precipitated on heating the solution, and 
re-dissolved on cooling. When boiled in water, the salt floats greasily about the 
surface. The propionate is easily soluble in alcohol even in the cold, and when the 
alcoholic solution is allowed to evaporate the propionate is deposited as a mass of 
minute spherical concretions with no appearance under the microscope of crystalline 
structure. 

The scandium propionate so obtained has the formula 

(C 2 H 6 COO) 2 ScOH. 

Analysis. 

15-978 grs. on ignition yielded 5'287 grs. of scandia, = 3'424 grs. of scandium. 

Theory. Experiment. 



Sc . . . 
OH ... 


. . 44-100 
' J163-088 


21-29 

7871 


21-43 
78-57 



207-188 100-00 100-00 






SIR WILLIAM CROOKES ON SCANDIUM. 33 

SCANDIUM BUTYRATE, 

* * 

(CH 3 -CH a -CH 2 -COO) 2 ScOH. 

When scandium hydroxide is heated with butyric acid, a white amorphous and 
difficultly soluble salt is produced. When boiled in water, the butyrate softens to a 
plastic mass, becoming hard and brittle on cooling. Like other scandium salts of the 
fatty acids, scandium butyrate is more soluble in cold than in hot water, and is 
precipitated from a cold solution on boiling. It is easily soluble in alcohol. The 
solution in cold water, evaporated over a water-bath, leaves a residue which under 
the microscope is seen to consist of minute spherical groups, radiating from a central 
nucleus. 

Analysis. 

6'251 grs. of butyrate yielded on ignition 1'82G grs. of scandia, = 1/18:2 grs. of 

scandium. 

Theory. Experiment. 



Sc 44-100 1875 18-91 

OH . 



2(C 3 H 7 COO) . 

235-220 100-00 lOO'OO 



SCANDIUM ISO-F.UTYRATE, 
3N >CH-COO\ScOH ) 2H a O. 



This salt is prepared in a similar manner to the butyrate, which it much resembles 
in appearance. It is more soluble in cold than in hot water, a saturated cold solution 
becoming thick and depositing amorphous flakes when heated. On cooling the liquid 
becomes clear again ; in this respect it closely resembles calcium butyrate. It is very 
soluble in alcohol and is precipitated by water from the alcoholic solution. 

The formula of the iso-butyrate differs from that of the butyrate in having two 
molecules of water of crystallisation : 

(C 3 H 7 COO) 2 ScOH,2H 2 O. 

Analysis. 

9-994 grs. of scandium iso-butyrate gave on ignition 2 '5 50 grs. of scandia, 

= T651 grs. of scandium. 
VOL. ccix. A. F 






34 



SIR WILLIAM CROOKES ON SCANDIUM. 

Theory. Experiment. 

16-52 



Sc 44-100 16-26 

OH -J 

2(C 3 H 7 COO) . . V227-152 8374 

2II 2 . . . J 

271-252 100-00 

SCANDIUM ISO-VALERATE, 



83-48 



100-00 



Scandium hydroxide is readily attacked by aqueous iso-valeric acid, forming a white 
amorphous salt, soluble in cold water, precipitated on boiling, and again dissolved on 
cooling. Dried over sulphuric acid the iso-valerate has the composition 

(C 4 H 9 COO) 2 Sc(OH),2H 2 0. 

Analysis. 

10-902 grs. of scandium iso-valerate left on ignition 2'493 grs. of scandia, 

Theory. Experiment. 

14-80 

85-20 



= 1'614 grs. of scandium. 



Sc 


44-100 


14-74 


OH - 


1 




2(C 4 H 9 COO) . . 
2H a O 


^255-184 


85-26 



299-284 



100-00 



100-00 



SCANDIUM OXALATE, 

Sc 2 (CA) 3 ,5H 2 0. 

Scandium oxalate comes down as a white crystalline powder when oxalic acid or 
ammonium oxalate is added to a solution of scandium. If much free mineral acid is 
present the precipitation is not immediate ; it begins by a cloudiness, which in a few 
minutes increases to a crystalline precipitate, a little scandium oxalate remaining in 
the solution. It is slightly soluble in water, weak acids, and more so in solution 
of ammonium oxalate. On boiling a mixed oxalate from wiikite in a solution 
of ammonium oxalate the portion dissolved was richer in scandium than the 
insoluble part. Attempts were made to effect a separation of scandia from the 
accompanying earths by making use of this fact. A mixed oxalate of crude earths 
was boiled in a strong solution of ammonium oxalate and then filtered, and this 



SIR WILLIAM CROOKES ON SCANDIUM. 35 

operation was repeated on the residue several times. Ultimately the most soluble 
and the least soluble earths were separated and their spectra photographed. 
The most soluble earth was nearly all scandia, with a little yttria, and traces of 
ytterbia, titania, and lime. The least soluble contained more yttria than scandia, but 
not mucli of either. By a repetition of this process it would not be difficult to effect 
a good separation of scandia and yttria ; I think the fused nitrate process is simpler 
and quicker. 

When crude scandium oxalate is boiled in a solution of ammonium oxalate a partial 
separation of the earths is effected, but it is less complete than when ammonium 
carbonate is used as a solvent. This is a very good method for separating scandia 
from zirconia, as hardly a trace of the zirconia is to be seen in the portion insoluble in 
hot ammonium oxalate. 

According to NILSON (' Comptes Rendus,' vol. xci., p. 121), the precipitated oxalate 
is slightly soluble in weak acids, and even in water. I have verified this observation ; 
care must be taken not to over-wash the oxalate, or loss will ensue, and the filtrates 
should be kept and worked again for scandium. 

The precipitated oxalate, dried in the air, contains 5 molecules of water. 

Analysis. 

(1) 22'445 grs., ignited at a yellow heat, left G'988 grs. of scandia. 

(2) 21 '873 grs. ignited left G'806 grs. of scandia. 

Theory. Experiment. 

7l)~ (2). 

ScA . . . 136-20 30-79 :JM3 3fl2 

3C 8 (>, . -]. : j OG . 08 09-21 G8-87 <!8'88 

5 H 2 O 



442-28 100-00 lOO'OO lOO'OO 

When the 5-hydrated oxalate is allowed to dry at the ordinary temperature over 
sulphuric acid, it loses 2 molecules of water and becomes a 3 -hydrate 



Analysis. 
7-G39 grs. left on ignition at a yellow heat 2'529 grs. of scandia. 



Theory. 


Experiment. 
33-11 
66-89 


ScA 

3CA 
3H 2 O . . ; 


:} 


136 
270 


200 
048 


2 


33 
66 


53 

47 


406 


248 

F 


100 


00 


100 


00 



36 



SIR WILLIAM CROOKES ON SCANDIUM. 



The 5-hydrate of scandium oxalate, dried in a hot-air oven at 100, loses 3 molecules 

of water and becomes a 2-hydrate 

Sc 2 (CA) 3 ,2HA 

Analysis. 

22'445 grs. lost 2-014 grs. of water. 

Theory. Experiment. 



ScA . . 
3CA . . 

2H,0 



352-200 
36-032 

388-232 



90-72 

9-28 

100-00 



91-03 

8-97 
100-00 



The hydrated oxalate, dried in vacua at 100 or in air at 140, loses all but one 
molecule of water and becomes a mono-hydrate 

Sc 2 (CA) 3 ,HA 

Analysis. 

(1) 32-118 grs. left on ignition 11756 grs. of scandia. 

(2) 15-694 grs. left 5 '8 15 grs. of scandia. 

(3) 8-304 grs. left 3'010 grs. of scandia. 

Theory. Experiment. 









(1). 


(2). 


(3). 


ScA 


. 136-200 


36-79 


36-60 


37-05 


36-25 


H 2 . . 


'T 234-016 


63-21 


63-40 


62-95 


6375 



370-216 



100-00 



100-00 



100-00 



100-00 



SCANDIUM SUCCINATE, 
CH 2 COOSc(OH) 2 



H a O = C 4 H 8 8 Sc 2 ,H 2 0. 



CH 2 COOSc(OH) 2 

This salt comes down as an insoluble white precipitate when dilute solutions of 
ammonium succinate and scandium nitrate are mixed. It also may be prepared by 
boiling scandium hydroxide in solution of succinic acid. It is slightly soluble in 
excess of either reagent, and is insoluble in water or alcohol. When dried in the air 
it forms a hard porcelain-like mass. 



SIR WILLIAM CROOKES ON SCANDIUM. 37 

Analysis. 

12713 grs. of scandium succinate heated for ten hours to 180 lost 0'822 gr. of 
water, and when ignited to full redness it left 6'089 grs. of scandia, = 3'943l 
grs. of scandium. 

Theory. Experiment. 



Sc,. . . " . 


88-200 


on-TR 




48'000-| 




H 8 


8'064 > 184'064 


f.Q-41 


O 8 


128'OOG J 




H,O 


18-016 


fi-91 



31-02 
62-51 

6-47 
290-280 100-00 100-00 



SCANDIUM PICRATE, 
{ C rt H 2 (NO.),0 } 2 ScOH, 1 4H 2 0. 

The hydroxide dissolves readily in warm solution of picric acid and separates in 
groups of long needle-shaped crystals of a rich yellow colour. When rapidly crystal- 
lised from a strong solution, the crystals form confused feathery masses, which on 
pouring off the mother-liquor turn to a felt-like mass difficult to drain. 100 parts of 
water at 20 dissolve 0'95 part of scandium picrate. At 9 the same quantity of 
water dissolves 0"37 part. Dried hy exposure to cold dry air the crystals have the 
composition shown above. 

The picrate cannot be detonated when wrapped in tin-foil and struck on an anvil 
with a heavy hammer. Heated in a dry test-tube it darkens, gives a slight 
sublimate, fuses, and at a little higher temperature faintly explodes, leaving a black 
flocculent residue, which burns off to pure white scandia at a red heat. 

The explosion, although not violent, is sufficient to blow some of the products out 
of the crucible. The scandia therefore was estimated by precipitating the hot solution 
with ammonia in considerable excess and well boiling the liquid before filtering. 
Unless this precaution is taken some of the picrate precipitates as such, and slight 
explosions occur when the precipitate is burnt. 

Analysis. 

(1) 27-497 grs. of picrate, dried at 100, gave off 5'906 grs. of water. 

(2) 27-497 grs. yielded 2'422 grs. of scandia, = T569 grs. of scandium. 



38 SIR WILLIAM CEOOKES ON SCANDIUM. 

Theory. Experiment. 



on 



5H S . . . J 



44-100 


573 


(1) and (2). 
571 


563-180 


73-20 


72-81 


162-144 


21-07 


21-48 



769-424 100-00 lOO'OO 

When the 14-hydrate is heated to 100, nine molecules of water go off, leaving a 

5 -hydrate 

{ C 6 H a (NO a ) 3 } 3 ,ScOH, 5H 2 0. 

Analysis. 

21-657 grs. of the picrate, dried at 100, gave 2'422 grs. of scandia, = 1'569 grs. of 

scandium. 

Theory. Experiment. 



Sc 44-100 7-26 7-24 

OH -I 

2{C 6 H 8 (NO a ) 3 O}. UeS'lSO 92-74 9276 

5H..O . 



607-280 100-00 lOO'OO 

SCANDIUM BENZOATE, 
(C 6 H 5 COO) 3 Sc. 

Scandium benzoate comes down as a white curdy precipitate on adding a solution 
of ammonium benzoate to scandium nitrate solution. On boiling the solution the 
precipitate collects as a crystalline powder. It is slightly soluble in water and 
alcohol, and easily soluble in dilute mineral acids. 

Analysis. 

12-303 grs. of scandium benzoate left on ignition 2'204 grs. of scandia, = T4272 

grs. of scandium. 

Theory. Experiment. 

( A 

Sc 44-10 10-83 11-60 

On 252-00-j 

H 15 15-12 I 363-12 89-17 88'40 

O 6 96-OOJ 

407-22 100-00 100-00 



SIR WILLIAM CROOKES ON SCANDIUM. 39 

SCANDIUM ORTHO-TOLUATE, 
5cOH,3H 2 O = (C 8 H 7 O 2 ) 2 ScOH,3H 2 O = C 16 H 15 O 5 Sc,3H 2 O. 

When scandium hydroxide is boiled with an excess of aqueous ortho-toluic acid, a 
salt is formed with the composition given above. It is a white crystalline powder 
insoluble in water. 

The same salt is formed by mixing solutions of ammonium ortho-toluate and 
scandium nitrate. It forms a voluminous white curdy precipitate, insoluble in hot or 
cold water. It contains 3 molecules of water, which are not driven off at 150. 

Analysis. 

12*316 grs. of scandium ortho-toluate dried in racuo over sulphuric acid left on 
ignition 2"171 grs. of scandia, = 1"4059 grs. of scandium. 

Theory. Experiment. 

Sc 44-100 11-45 11-42 



H 15 . . . 
5 . . . 
3H 2 O . . . 54-048 J 





44-100 


11-45 


192-0001 






15-120 1 
80-000 f 


341-168 


88-55 



385-268 100-00 JOO'OO 

It is seen that this ortho-toluate lias the same percentage composition as the 
phenyl-acetate, but differs in structural constitution. 

BASIC SCANDIUM ORTHO-TOLUATE. 

When scandium hydroxide is boiled with solution of ortho-toluic acid, keeping the 
hydroxide in slight excess, a basic scandium ortho-toluate is formed. It can be 
decanted easily from the excess of hydroxide, which is of greater density ; it is 
anhydrous and has the composition 

Sc(OH) 3 = 2C 8 H 7 3 Sc + Sc(OH) : , 

This basic ortho-toluate is a white powder, insoluble in water and alcohol, but 

easily soluble in dilute acids. 

Analysis. 

(1) 6 "402 grs. of basic scandium ortho-toluate, dried over sulphuric acid in vacuo, 

left on ignition 2711 grs. of scandia, = 17556 grs. of scandium. 

(2) 7'631 grs. of basic scandium ortho-toluate left on ignition 3'219 grs. of scandia, 

= 2'0846 grs. of scandium. 



40 



Sc 3 

Q 

H 17 

9 



SIR WILLIAM CEOOKES ON SCANDIUM. 
Theory. 



132-300 27-25 
192'000-j 

17-136 > 353-13(5 72'75 
144-OOOJ 



485-436 100-00 



Experiment. 



(1). 
27-42 

72-58 



(2). 
27-32 

72-68 



100-00 100-00 



The above basic salt is formed by the union of two molecules of the ortho-toluate, 
C 8 H 7 O 3 Sc, with one molecule of scandium hydroxide, Sc(OH) 3 . 



SCANDIUM META-TOLUATE, 

= (C 8 H 7 O a ) 3 ScOH,3H 3 = C 18 H 1B O 6 Sc,3H 3 O. 

This salt is formed by double decomposition between ammonium meta-toluate and 
scandium nitrate solutions. It comes down as a voluminous white curdy precipitate, 
insoluble in water. 

Analysis. 

IS'702 grs. of the meta-toluate, dried in racuo over sulphuric acid at the ordinary 
temperature, left on ignition 2'673 grs. of scandia, = 17310 grs. of scandium. 



Theory. Experiment. 


Sc . . . . 


44-100 11-45 11-02 


C 16 . . . " . 192-000" 





H, B .... 15-120 


341-168 88-55 88'98 


O 5 . . . . 80-000 




3H 3 O . . . 54-048^ 





385-268 



100-00 



100-00 



SCANDIUM PARA-TOLUATE, 
2 ScOH,3H 2 O = (C 8 H 7 O 2 ) 2 ScOH,3H 2 = C 16 H 18 O 6 Sc,3H 2 O. 

Scandium para-toluate is formed by double decomposition in the same manner as 
the ortho-toluate, and has the same composition. It separates with three molecules 
of water, which are not driven off at 150. It is a white curdy precipitate insoluble 
in hot' or cold water. 



SIR WILLIAM CROOKES ON SCANDIUM. 41 

Analysis. 



12-332 grs. of scandium para-toluate on ignition left 2'141 grs. of scandia, 


= 1-3865 grs. 


of scandium. 






Theory. 

t . \_ 


Experiment. 


Sc . . . 


44-100 


11-45 11-24 


c ia . *. . 


. 192-000] 




H 16 . . . 


15-120 [ 




B . . . 


80-000 [ 


88-55 8876 


3H 3 (.) . . 


54-048 j 





385-268 100-00 lOO'OO 



SCANDIUM PHENYL-ACETATE, 
(CJI 5 CH 2 C(X)) a ScOH,:3lI,< ) = C 1(i IT,,( ),Sc,:)IU ). 

Scandium hydroxide is readily attacked l>y aqueous phenvl-acetic acid, with the 
formation of a white insoluble phenyl-acetate. The salt thus prepared lias, however, 
a tendency to become more basic, and a better way to prepare it is by double 
decomposition between ammonium phenyl-acetate and scandium nitrate. When 
moderately dilute and hot solutions of these salts are mixed and the whole boiled, 
the phenyl-acetate comes down chiefly on the sides and bottom of the beaker, ;nid 
adheres to the glass with great pertinacity. It can onlv be removed with difficulty 
and risk of breakage. The deposit on the glass looks like warty concretions and 
under a high power appears crystalline. It is almost insoluble in hot or cold water, 
and is insoluble in alcohol. 

When double decomposition between scandium nitrate and ammonium phenyl- 
acetate is effected in the cold, the salt comes down as a white curdy precipitate which 
does not adhere to the glass, and can be washed easily with warm water; boiling 
water, however, causes it to cohere \\ith contraction. The. dry salt when heated 
softens and can be pressed into a pasty mass. It does not fuse at a temperature at 
which decomposition begins. 

Analysis, 

(1) 13"584 grs. of scandium phenyl-acetate precipitated from hot solutions and 

washed with boiling water, filtered and dried at 100 till the weight was 
constant, yielded on ignition 2'396 grs. of scandia, = T551G grs. of scandium. 

(2) 9'458 grs. of scandium phenyl-acetate precipitated from cold solutions, washed 

and dried at 100 to a constant weight, gave on ignition To 71 grs. of scandia, 
= 1'0821 grs. of scandiinn. 
VOL. CCIX. A. G 



42 



SIR WILLIAM CEOOKES ON SCANDIUM. 
Theory. 



Experiment. 



Sc 

C w 192-000] 

H ]8 15-120 ' 

O 5 80-000 

3H 3 O .... 54-048 j 



44-100 



11-45 



(1). 
11-42 



}- 341-168 88-55 



385-268 



100-00 



88-58 



100-00 



(8). 

11-44 



88-56 



100-00 



Attempts to estimate the water were unsuccessful, as the phenyl-acetate turned 
brown and commenced to decompose when heated above 160, at which temperature' 
the whole of the three molecules of water were not expelled. 

SCANDIUM PYROMELLITATE, 
C () ?I 3 {CO()Sc(()H) a } 4 2H a O - Sc 4 C 10 H 10 16 ,2H 2 0. 

This salt comes down when ammonium pyromellitate is added to a solution of a 
soluble scandium salt. Tt is formed also by allowing pyromellitic acid to act on 
scandium hydroxide with the aid of gentle heat. Scandium pyromellitate is a white 
amorphous powder, insoluble in water and alcohol, but soluble in dilute acids. 

Of the two molecules of water of hydration one is driven off at 100 and the 
remaining molecule at 140. The dried salt can be heated to 220 without 

decomposition. 

Analysis. 

(1) 14-304 grs. of scandium pyromellitate dried at 1 40 for some hours lost 0'847 grs. 

of water ; when ignited to full redness, treated with nitric acid, and ignited 
again, it left 6'515 grs. of scandia, = 4'2190 grs. of scandium. 

(2) 11 "485 grs. of scandium pyromellitate dried at 100 lost 0"350 gr. of water, 

and, when ignited as above, left 5 '170 grs. of scandia, = 3 "3480 grs. of 
scandium. 

(3) 7"614 grs. of scandium pyromellitate heated to 220 for three hours lost 

0'464 gr. of water, and, when ignited as already described, left 3'501 grs. of 
scandia, = 2 '2672 grs. of scandium. 



Theory. 



Experiment. 




176-400 
386-080 

18-016 
18-016 



598-512 



29-47 
64-51 

3-0 
3-C 

100-00 



(1). 

29-50 

64-58 
5-92 

100-00 



(2). 
29-15 

64-83 

J 3-05 "I 
12-97J 

100-00 



(3). 

29-78 

64-13 
6-09 

100-00 



SIK WILLIAM CROOKES ON SCANDIUM. 43 



SCANDIUM CAMPHORATE, 



The camphorate is prepared by heating scandium hydroxide with a slight excess of 
camphoric acid and water. The hydroxide is easily attacked and converted into an 
insoluble camphorate. It may be prepared also by precipitating a solution of scandium 
nitrate with a solution of ammonium camphorate. In either case it forms an insoluble 
white precipitate, which, after thorough washing and drying at 100, has the 
composition given above. 

Scandium camphorate is anhydrous and insoluble in water and alcohol. It is 
easily soluble in dilute mineral acids. When dry it is very electrical, and an attempt 
to powder it sends it flying out of the mortar. If it is put warm between two watch- 
glasses, and the lower glass is gently rubbed on the outside with the finger, the path 
of the finger is marked by a flight of camphorate from the lower to the upper glass, 
where it sticks. This peculiarity makes it not easy to perform the preliminary 
operations of drying, transferring, and weighing, preparatory to its quantitative 
analysis. 

Gradually heated to redness, the camphorate at first blackens with carbon. At a 
red heat this burns off, leaving a white residue of scandia. 



Analysis. 

(1) 18'191 grs. of the camphorate, dried at 100, yielded on ignition 4772 grs. of 

scandia, = 3'0902-grs. of scandium. 

(2) 17'921 grs. of the camphorate yielded on ignition 4719 grs. of scandia, 



= 3'0559 grs. of scandium. 



Theory. Experiment. 



(i). (*) 
Sc 44-10 17-01 16-99 17'05 

C 10 120-00^ 

H 16 15-12 I 82-99 83'01 82'95 

O 5 80'OoJ 



259-22 100-00 lOO'OO lOO'OO 



G 2 



44 SIR WILLIAM CROOKES ON SCANDIUM. 



Added April 30th, 1908. 

Scandium is remarkable inasmuch as its existence was foretold by MENDELEEFF,* 
and called by him ekaboron, eight years before its actual discovery by NILSON. To-day 
I may be permitted to indulge still further in speculations on the genesis and 
degradation of the chemical elements speculations which a few years ago might have 
Iteen derided even by a learned Society. But the undoubted fact of the production 
of helium from radium, the probability that chemical elements of high atomic weight 
are slowly breaking up into bodies of lower atomic weight, and the suspicion that 
some well-known chemical elements of low atomic weight are degradation products, 
embolden me to speculate on the past history and genesis of scandium. 

In 1898 I brought before the Eoyal Society a scheme of the arrangement in Space 
of the chemical elements in which scandium was seen to fall in place between boron 
and yttrium. I hesitated to introduce ytterbium into the scheme, as its atomic 
weight was not known with sufficient accuracy to enable it to be properly placed. 
To-day it is seen to fill a gap below yttrium, and the group is: Boron, scandium, 
yttrium, ytterbium. These four elements have a close relationship, thus : 

B atomic weight . .... I TO x 1(5 == 176'0 

Se 44-1 . x 4 == .176-4 

Y 89-0 x 2 = 178-0 

Yb m-0 x 1 = 173-0 

In reference to this table it must be remarked that the atomic weight of scandium 
certainlv is not known with absolute accuracy, the '1 being little more than a guess. 
Yttrium, moreover, is now seen to be very liable to contain scandium ; when 
CLEVE determined its atomic weight it was impossible, without further refined 
spectroscopic examination not available at that date to detect in it the trace of 
scandium sufficient to lower the atomic weight by one unit. Ytterbium certainly is 
too low, for URBAIN recently has announced the discovery in it of an element of a 
lower atomic weight ; this being removed might raise the atomic weight of ytterbium 
a few units. With these reasonable corrections the last column will not be far from 
the same whole number, 17G. 

The frequent occurrence of the triad ytterbium, yttrium, and scandium in a very 
limited group of rare minerals may be explained by assuming the instability of 
ytterbium, the atom of highest weight, and letting it split into two atoms, when 
yttrium would be produced. Assume the same action to take place with yttrium, its 
splitting up again into two atoms would produce scandium ; and scandium (" eka-boron, 

* D. I. MENDELEEFF, " A Natural System of the Elements, and its Application to the Indication of the 
Properties of Undiscovered Elements," ' Russ. Chem. Soc. Journ.,' 1871, iii., pp. 25-56. 



SIR WILLIAM CROOKES ON SCANDIUM. 45 

next in order to boron ") would ultimately form boron by a quadruple sub-division. 
The comparatively small quantities of ytterbium and scandium in these minerals may 
easily be accounted for by the assumption that they are more unstable forms of 
matter than yttrium and boron. 

The fact that these bodies give totally distinct line spectra has not the significance 
it formerly was supposed to have, for now we know of different line spectra given bv 
the same body. Argon, with its red and blue spectra, is a case in point, and 
GOLDSTEIN, as a result of his work on the spectra of Cs, lib, and K, has come to the 
conclusion that the property of emitting two separate line spectra is a general one. 
Moreover, between the line spectra of radium, uranium, and helium bodies which 
are supposed to be associated genetically there is no similarity or line in common. 



46 SIR WILLIAM CROOKES ON SCANDIUM. 



BIBLIOGRAPHY OF SCANDIUM. 

" On Scandium, a New Element." L. F. NILSON. ' Berichte,' 1879, No. 6 ; ' Comptes 

Rendus," March 24, 1879, vol. Ixxxviii., p. 645; in abstract in 'Chemical 

News,' August 15, 1879, vol. xl., p. 76. 
" On Scandium." P. T. CLEVB. ' Bull. Soc. Chim. de Paris,' June 5, 1879, vol. xxxi., 

p. 486. 
"On Scandium." P. T. CLKVE. 'Comptes Rendus,' August 18, 1879, vol. Ixx.xix., 

p. 419 ; in full in ' Chemical News,' October 3, 1879, vol. xl., p. 159. 
" Atomic Weight of Scandium, and on certain of its Characteristic Salts." L. F. 

NELSON. 'Comptes llendus,' July 12, 1880, vol. xci., p. 118; in abstract in 

' Chemical News,' August 1 3, 1880, vol. Ixii., p. 83. 
" Atomic Weight and certain Characteristic Compounds of Scandium." L. F. NILSON, 

' Berichte,' vol. xiii., No. 13. 
" Brilliant Spectral Hays of the Metal Scandium." II. THALEN. ' Comptes Rendus,' 

July 5, 1880, vol. xci., p. 45; 'Chemical News,' July 30, 1880, vol. xlii., 

p. 60. (THALEN only gives the wave-lengths of lines in the visible portion of 

the spectrum.) 
" Spectral Researches on Scandium, Ytterbium, Erbium, and Thulium." TH. THALEN. 

' Journal de Physique ' ; ' Chemical News,' May 11, 1883, vol. xlvii., p. 217. 
W. CROOKES. " On Radiant Matter Spectroscopy : Examination of the Residual 

Glow." ' Proc. Roy. Soc.,' February 1887, vol. xlii., p. 111. "Scandium, 

either in the form of earth or sulphate, phosphoresces of a very faint blue 

colour. Addition of lime does not bring out any lines." 
" The Arc Spectrum of Scandium, and its Relation to Celestial Spectra." By 

Sir NORMAN LOCKYER and F. E. BAXANDALL. ' Proc. Roy. Soc.,' February, 

1905, vol. Ixxiv., p. 538. 
G. URBAIN ('Journal de Chimie-Physique,' February, 1906, vol. iv., p. 64) gives a 

passing reference to scandium as follows: "In none of my fractions have I 

been able to observe the presence of scandium. I am led to think that this 

element does not belong to the group of rare earths, properly so-called. 

Sir W. CKOOKES (' Chemical News,' vol. xci., p. 61) thinks he has detected 

this element in my gadolinia. [Quite true. W. C.] The statement is denied 

by EBERHARD (' Zeit. Anorg. Chemie,' xlv., p. 374)." 






Sir William Crookes. Phil. Trans., A, vol. 209, Plate 1. 

THE SCANDIUM SPECTEUM. SELECTED GROUPS OF CHARACTERISTIC LINES. 

i'o economise space and avoid unnecessary complications, I give photographs of only those parts of the spectrum containing the most 
i ninent scandium groups. The upper half of each strip shows the iron lines used as standards, with their wave-lengths according to 
VIAND'S measurements. The lower halves contain the scandium linos, with their wave-lengths calculated from the iron standards. 
1'here are also many strong lines in the ultra-violet spectrum of scandium between A 3535 -865 and A 2300. I have not completed the 
, .suremcnts of these lines, and their description must form the subject of a subsequent communication. 



Ss 
& s 



II 



a 

s 



i is 






pi I 



III I 



I 



8.f-pectrum of crude rare earths from keilhauite, also photographed 7. Spectrum of crude rare earths from enxenite, also photographed 
in the same position as in Spectrum 5. It was from the rare earths in the same position as in Spectrum 5. It was from euxenite that 

from keilhauite that CLEVE prepared scandium. NII.SON" first extracted scandium. 



at 




1 P S ^ 

] IN r-*j , 

!S 3 S 



5. 



Sp& trum of crude rai'e earths from wiikite, photographed in the 5. Group of linos between A. :5(;.">I '.)()] and A 3535 -si;."). This is the part 

Set " ' 

01 

ill' 



me position as in Spectrum 5. In addition to the dominant and 
:uer lines of scandium, which are marked in wave-lengths, there 
! seen lines of yttrium and one strong line of ytterbium. 



of the spectrum which I photograph when minerals are being 
examined for scandium. The "dominant line.'' A 3(1 1 .'i Ulj.j occurs 
here between the iron lines A 36 1 S !) 1 !J and A .'((>( )'J -(J(J8. 






4. 3 



s a i 



4. Group of lines between A 4082 '590 and A 3843-163. 



3. Group of lines between A 44 15- 722 and A 4122-613. 




2. Group of lines between A 5087-1 and A 4672-590. 







ssss 



1. 



1. Group of visible lines between A 6305-231 and A 5527-033. 



In the part of the spectrum shown on strips 1 and 2 there are no iron lines suitable for standards. Here, therefore, I have used some good 
ies of zinc, cadmium, and mercury. Attention is drawn to the comparative intensities of the yttrium lines and the dominant line of scandium 

tl e spectra from the wiikite, euxenite, and keilhauite earths. The spectrum of the earths from gadolinite is not given, as the dominant line 
t sc andium in it is too faint to be reproduced. 



III. The Spectrum of Scandium, and its Relation to Solar Spectra. 

By A. FOWLER, A.R.C.S., F.R.A.S., Assistant Professor of Physics, Imperial, College 
of Science and Technology, South Kensington. 

Communicated by Sir WILLIAM CROOKES, D.Sc., F.R.S. 
Received June 23, Read June 25, 1908. 

INTRODUCTORY. 

THE present investigation of the spectrum of scandium was undertaken in connection 
with the work on the spectra of sunspots and .solar prominences with which I have 
been occupied during the past few years. The presence of scandium in spots and 
prominences was already well known, but all the desired information \vitli respect to 
the positions and characteristics of the various lines could not be gathered from 
published tables. 

THALEN'S observations of the spark spectrum* extend from 4247 to (5305, but 
though his intensities give a useful term of comparison in some cases, the wave- 
lengths lack the precision necessary for use with modern solar tables, and a consider- 
able part of the red is omitted. A few of the Fraunhofer lines were identified with 
scandium by RowLAXD,t but, probably for want of suitable material for the 
production of the scandium spectrum, the comparison was far from complete. More 
extensive observations of the arc and spark spectra have been made by EXNER and 
HASCHEK,! but, as they extend no further into the visible spectrum than 4744, they 
scarcely enter the region in which the spectra of spots and prominences are best 
known. The arc spectrum has been further studied by LOCK.YER and BAXANDALL, 
but here again the region from 5718 to the red end was not included, and but little 
attempt was made to classify the lines. 

Attention was specially drawn to the need for the re-determination of some of 
THALEJST'S wave-lengths in the course of a discussion of some observations of the 
spectra of sunspots in the region C to D,|| when it was suggested that two very 

* ' WATT'S Index of Spectra,' p. 125. 

t 'Preliminary Table of Solar Spectrum Wave-lengths,' Chicago, 1896. 
t ' Welleulangen-Tabellen ' (Leipzig und Wien, 1904). 
'Boy. Soc. Proc.,' vol. 74, p. 538 (1905). 
|| ' Monthly Notices, E.A.S.,' vol. 65, p. 211 (1905). 
VOL. CCIX. A 443. 5.11.08 



48 ME. A. FOWLEK ON THE SPECTEUM OF SCANDIUM, 

prominent spot lines recorded at 6210'90 and 6306"02 might be due to scandium. 
THALEN'S wave-lengths for strong scandium lines near these positions were 6210'0 
and 6304'0 or 6211/0 and 6305'! when corrected to ROWLAND'S scale and the 
identifications seemed probable in consequence of the undoubted presence in spots of 
the scandium line 5 672 '05. The wave-length 6306 '02 was adopted by Father CoRTlE 
and myself because the spot line could not be distinguished from the telluric oxygen 
line in that position with the instruments employed, but with greater dispersion 
MITCHELL* and NEW ALL f subsequently identified the spot line with ROWLAND'S solar 
line 6305 '88. Observations for checking these identifications were long delayed on 
account of the difficulty of obtaining a specimen of scandium with which to produce 
the spectrum, but a few months ago, after an examination of several minerals reputed 
to contain rare earths, a strong scandium spectrum was obtained from a piece of South 
African euxenite. The spectrum obtained in this way was admixed with lines and 
bands of calcium, yttrium, and other substances, but it was quite adequate for the 
re-determination of wave-lengths, assuming the lines to have been correctly attributed 
to scandium by THALEN. Measurements of photographs of the arc spectrum of the 
mineral removed all doubt as to the precise correspondence of the spot lines 6210'90 
and 6305 '88 with strong lines of scandium first tabulated by THALEN. 

The scandium lines came out so clearly in the spectra of some of the fragments of 
euxenite that I was induced to carry the inquiry a stage further, in view of the 
peculiar selection of lines for representation in the solar spectrum and in sunspots. 
As I have previously remarked : J " The scandium lines which appear in the spots are 
among the strongest in the arc spectrum, while the possible coincidences with the 
fainter lines are so few as to be probably accidental. At the same time there are 
some strong arc lines which are not intensified in the spots ; it is a noticeable fact 
that these are more intense in the solar spectrum than those which appear in the 
spots, and the probability is that all of them, like 5527 '03, are related to the enhanced- 
line class." There is a similar selection of lines in the chromospheric spectrum, as also 
remarked by LOCKYER and BAXANDALL, but the lines are different from those which 
appear in spots. 

Similar differences of behaviour have been noted in the case of other elements, but 
scandium appeared to be rather an extreme example, and further study of the varying 
intensities of its lines promised to be of value, not only in identifying particular lines 
with scandium, but in helping to establish the principles to be followed in assigning 
solar lines of different classes to metallic origins. 

On comparing the euxenite spectrum with the scandium arc recorded by LOCKYER 
and BAXANDALL it was at once evident that the intensities assigned in the two cases 
were often widely different. For example, the two lines 5527 and 5672 are given as 

* ' Astrophys. Jour.,' vol. 22, p. 27 (1905). 

t 'Monthly Notices, E.A.S.,' vol. 67, p. 167 (1906). 

J 'Trans. Int. Sol. Union,' vol. 1, p. 228 (1906). 



AND ITS RELATION TO SOLAR SPECTRA. 49 

10 and 9 respectively in the scandium arc, while in the euxenite arc the former was 
less than half the intensity of the latter. Such differences as this are no doubt to be 
accounted for by differences in the conditions of experiment. LOCKYER and 
BAXANDALL worked with scandium oxalate, and probably obtained what may be 
properly considered the arc spectrum of the element. In euxenite, on the other hand, 
the presence of calcium and other substances tended to produce the condition of a 
" naming arc," and the scandium lines doubtless appeared with intensities approxi- 
mating to those proper to the "arc-flame" or "flame" spectrum. That is, in 
euxenite the presumably "enhanced lines"" were notably weakened as compared 
with their intensities in the true arc spectrum. Further evidence that these 
weakened lines were enhanced lines was given in some cases by comparison with the 
spark intensities of THALEN. 

Although a comparison of intensities estimated by different observers is often apt 
to be misleading, the " inversions " in the case of several scandium lines were 
sufficiently pronounced to support the previous deduction, from the behaviour of other 
elements, that flame lines were strengthened and enhanced lines weakened in spots, 
while the enhanced lines might appear alone in the upper chromosphere. 

At this stage of the investigation I was fortunate enough to receive the valuable 
assistance of Sir WILLIAM CKOOKES. In reply to an inquiry about two years ago 
Sir WILLIAM CROOKES informed me that scandium was extremely scarce, and that, 
although he had been carefully collecting residues for some time, he had not then 
obtained sufficient for a satisfactory examination of the spectrum. By the end of last 
year, however, when I acquainted him with the results obtained from euxenite, lie not 
only informed me that he had succeeded in collecting and purifying a considerable 
amount of scandia (Sc 2 O 3 ), but very generously placed half a gramme of the substance 
at my disposal. It thus became possible to make a much more complete catalogue of 
scandium lines, and a more satisfactory investigation of the behaviour of the lines 
under varying experimental conditions. As Sir WILLIAM CROOKES was himself 
occupied with the spark spectrum, the electric arc was exclusively employed in my 
own work, but the conditions were varied so as to give in some cases an approach to 
the spark spectrum, and in others to the flame spectrum. 

The Spectrograph Employed. 

The photographs were taken with a spectrograph of Littrow form, having a lens of 
12 feet focal length, and one prism of GO for which /A D is l'G4G7. The plates are 
12 inches in length, and show satisfactory definition throughout, the region covered 
being 3930 to 4G70, or 4G70 to GGOO, according to the position of the mirror which 

* " Enhanced lines " are lines which are relatively strengthened in passing from the arc to the spark 
(LOCKYER). 

VOL. CCIX. A. H 



50 ME. A. FOWLEE ON THE SPECTEUM OF SCANDIUM, 

returns the light through the prism. At 6600 the linear dispersion is 127 tenth- 
metres to the millimetre, while at 3930 it increases to 1'8 tenth-metres per millimetre. 

The determination of wave-lengths was made in the usual manner with the aid of 
the Cornu-Hartmann interpolation formula for prismatic spectra, a separate equation 
being computed for each region of 100 to 200 tenth-metres. Lines in a comparison 
spectrum of iron, slightly overlapping that of scandium, were used as standards, 
ROWLAND'S solar wave-lengths for corresponding lines being adopted. Numerous 
iron lines were included in the measures, and small corrections, depending upon the 
degree of agreement between the computed and observed values of these extra lines, 
were applied to the resulting wave-lengths for scandium. 

On comparison with LOCKYER and BAXANDALL'S wave-lengths, it was found that 
there were small systematic differences in some parts of the spectrum which persisted 
after repeated measurements of different plates. It was accordingly thought desirable 
to take another photograph in which iron was mixed with scandia, so that there 
should be no possibility of a relative displacement of the comparison lines. The 
previously deduced wave-lengths were fully confirmed by this procedure. 

For all but the weakest lines it is hoped that in the part of the spectrum more 
refrangible than D the wave-lengths are correct to within two or three hundredths of 
a tenth-metre, while on the red side of D, in consequence of the smaller dispersion, 
the errors may be somewhat greater. 

The Arc Spectrum. 

The arc .spectrum was produced in the ordinary manner by introducing a small 
quantity of scandia between carbon poles, the current being obtained from the 
110-volt lighting circuit. The P.D. between the poles was about 40 volts, and the 
current 8 amperes. The scandia did not volatilise very readily, and with the small 
amount of material that one felt justified in using, carbon flutings were also present 
in the spectrum and tended to conceal some of the fainter metallic lines. Better 
results were obtained by mixing a little silicate of soda or silicate of potash with the 
scandia, the carbon flutings being then practically eliminated, and a good spectrum 
secured with a very small amount of scandia. The few impurity lines introduced in 
this way were readily recognised, and were less objectionable than the multitude of 
lines composing the carbon flutings. To avoid unnecessary waste of so rare a 
substance, the arc was usually enclosed in a glass globe, so that the residues might be 
collected and the scandia subsequently separated by chemical treatment. 

A list of the arc lines between K and C is given in Table I., at the end of this 
paper. The intensities are on a scale such that 10 corresponds to the brightest lines, 
and 1 to lines which are just well visible on negatives taken with moderate exposures ; 
very faint lines, which only appeared clearly on strong photographs, are indicated, on 
ROWLAND'S plan, by and 00. The estimates of intensity are based on an exami- 



AND ITS RELATION TO SOLAR SPECTRA. 51 

nation of several negatives made with varying exposures, as there is a tendency for 
small differences in the brighter lines to be effaced by long exposure. It should be 
understood, however, that the intensities estimated in this way indicate little more 
than the relative brightnesses of the lines in the same part of the spectrum. 

The enhanced lines, of which 5527 - may be taken as a type, fluctuated consider- 
ably in intensity in the arc and appeared differently on different photographs. 
Nevertheless, all the lines of this class varied together, so that there was no change 
in the intensities of the enhanced lines with respect to each other, but only with 
respect to the arc lines. 

The flutings which occur in the arc spectrum are dealt with under a separate 



heading. 



The Arc in Hydrogen. 



The well-known experiments of CREW* and othersf have shown that, when the arc 
is surrounded by an atmosphere of hydrogen, the spectrum changes in the direction 
of that given by the spark. Flame lines are relatively reduced and enhanced lines 
increased in intensity. 

Photographs of the scandium arc in hydrogen, at a pressure of about 75 mm., were 
taken, and the enhanced lines were readily identified by their strengthening when 
observed in this way. The use of the arc in hydrogen probably does not reveal 
anything more than the spark as regards the line spectrum, but is sometimes a 
convenient method of arriving at the same result. Scandia, however, was rather 
refractory under this treatment, and it was not found possible to avoid the presence 
of carbon flutings in the photographs. 

An interesting result of this experiment was the complete disappearance of the 
scandium flutings which form such a striking feature of the arc in air. 

Although the enhanced lines as a whole were brightened when the. arc was passed 
in hydrogen, their relative intensities were not appreciably different from those found 
in the ordinary arc. It would therefore serve no useful purpose to give separate 
estimates of the intensities of the lines in hydrogen. Following LOCKYER'S notation, 
the enhanced lines are indicated, in the second column of Table L, by the letter " p" 
following the intensity number, p being an abbreviation for " proto," so that pSc 
signifies " protoscandiurn," and so on. 

For the more refrangible part of the spectrum (3930 to 4670) the enhanced lines 
were identified first by their behaviour in the arc-flame, as explained under the next 
heading, and checked by reference to a photograph of the spark spectrum which was 
kindly forwarded to me by Sir WILLIAM CROOKES. 

It should be noted that the enhanced lines of scandium differ from those of iron, 
titanium, and certain other elements, in exhibiting themselves with relatively great 

* ' Astrophys. Jour.,' vol. 12, p. 167 (1900). 
t ' Roy. Soc. Proc.,' vol. 72, p. 253 (1903). 
H 2 



52 ME. A. FOWLER ON THE SPECTRUM OF SCANDIUM, 

intensity in the ordinary arc spectrum, as well as in the spark spectrum. Why this 
should be so is not quite clear, but scandium is not a'lone in this behaviour, as 
reference to the spectra of calcium, strontium, and barium will show, though this 
point has received little attention hitherto. In the case of the iron arc, the enhanced 
lines are almost insignificant in the integrated light, but they appear with consider- 
able intensity close to the positive pole, and with less intensity near the negative 
pole.* It would seem that in the case of scandium and the other elements named 
the region of the arc in which enhanced lines are produced is of greater extent than 
in the case of such substances as iron. However that may be, the H and K lines of 
calcium, the lines 4078, 4215 of strontium, the lines 4554, 4934 of barium, and the 
lines of scandium in question, have all the other characteristics of enhanced lines and 
may be properly regarded as such. They are weakened in the flame, relatively 
brightened in the spark, and are isolated from the other lines of the arc spectra when 
observed in the upper chromosphere and in certain stellar spectra. The enhanced 
lines are, in fact, to be regarded as forming a distinct spectrum of scandium, which 
may or may not co-exist with the other lines according to circumstances. A separate 
list of these lines is given in Table V. 

The Arc-Flame Spectrum. 

An economical method of producing an approximation to the flame spectrum was 
suggested by the observations of the spectrum of euxenite, to which reference has 
already been made. It was felt that the material available was inadequate for the 
effective use of the oxyhydrogen flame, or even for the comparatively long exposures 
required for the outer part of the flame of an ordinary arc. 

The method of purposely introducing other substances into the arc was therefore 
adopted, the idea being to produce a " flaming arc " without unduly increasing the 
number of impurity lines in the spectrum. For this purpose silicate of soda, silicate 
of potash, and sodium chloride were separately tried and found to be effective if used 
in sufficient quantity. A very long "arc" was thus obtained (the P.D. between the 
poles falling to about 30 volts), and photographs were secured in which the enhanced 
lines, including even the strong line 5527, were reduced to mere traces. In the blue 
end of the spectrum the strong enhanced lines were much enfeebled in other 
photographs covering this region, and it might have been possible to abolish these 
lines also if more material had been available for continued experiments. 

It should be mentioned that the spectrum fluctuated considerably, the enhanced 
lines occasionally coming in as in the ordinary arc, but, so ,far as possible, the exposures 
were only made in the intervals when visual observations showed that the enhanced 
lines were absent from the spectrum. The desired condition could be restored, in a 
general way, by adding more of the supplementary substance. 

* FOWLER, ' Monthly Notices R.A.S.,' vol. 67, p. 154 (1906). 



AND ITS RELATION TO SOLAR SPECTRA. 53 

A valuable confirmation of the identification of the enhanced lines was thus obtained, 
but as regards the remaining lines it can only be said that, within the limits of these 
experiments, the brighter arc lines survived in the " arc-flame " with little change in 
their relative intensities. 

The arc-flame spectrum may accordingly be regarded as consisting of the brighter 
lines of the arc spectrum, except that the enhanced lines (indicated by " p " in the 
second column of Table I.) are entirely absent. Separate estimates of intensities in 
the arc -flame* would therefore be superfluous, and might be misleading. The principal 
lines of the arc-flame spectrum are brought together in Table IV. 

Impurities. 

Allowing for the impurities known to be introduced by the use of carbon poles, or 
by admixture with other substances for the special purposes already mentioned, there 
is no evidence of any considerable impurity in the scandia so carefully prepared by 
Sir WILLIAM CROOKES. In the blue end of the spectrum, thanks chiefly to the 
admirable work of EXNER and HASCHEK, fairly complete data are available for the 
detection of such impurities, and in this region at least, with the exception of the 
yttrium line 4883'8, all the probable impurity lines are extremely faint. In the less 
refrangible parts of the spectrum the existing records do not permit the identification 
of impurities to the same extent, but from the evidence afforded by the blue end it is 
unlikely that any but very faint lines will turn out to be due to substances other 
than scandium. 

A list of the lines rejected as impurities (excluding those of calcium, barium, iron, 
sodium, and potassium introduced in the course of the observations) is given in 
Table II. It will be seen that the principal impurity lines are attributed to yttrium, 
ytterbium, thorium, and cerium, while a few lines are probably due to samarium, 
gadolinium, and europium. Other faint lines at present included in the general list 
of scandium lines, Table I., may subsequently have to be rejected as impurity lines, 
more especially those which occur in the region less refrangible than 4700. 

As will be seen from Table I., not more than two of the lines given by EXNER and 
HASCHEK do not occur in Sir WILLIAM CROOKES' scandia, while several of LOCKYER 
and BAXANDALL'S lines have not been found. The scandium oxalate with which the 
latter observers worked was admittedly impure, and it would appear probable that 
lines given by them which do not occur in my own list are not due to scandium. As 
no list of rejected lines was given by LOCKYER and BAXANDALL, it cannot be 
determined to what extent the additional lines in my table should be attributed to 
impurities on similar grounds. 

As already remarked, impurity lines in my own catalogue are probably only to be 
expected among those of very low intensity, but several well-marked lines are not 
recorded by LOCKYER and BAXANDALL. In reply to an inquiry as to three of these 



54 MR. A. FOWLER ON THE SPECTRUM OF SCANDIUM, 

lines, 5210'7, 5219 - 7, and 5375'5, all of which were given as scandium lines by 
THALEN, Sir NORMAN LOCKYER has kindly informed me that weak lines in these 
positions were found on the Kensington photographs, but not included in the published 
list. The line at 52 10 '7 was almost masked by the shading from the strong silver 
line 5209 - 6 arising from the silver poles employed for the arc, and this probably 
accounts for its being passed over. In the case of 52 19 '7 the line was marked on the 
photograph as an impurity, but the record as to the substance to which it was 
attributed has been misplaced. The third line, 5375'5, was omitted as being possibly 
due to thorium, for which THALEN gives a fairly strong line at 5374 '6, or 5375 '6 when 
corrected to ROWLAND'S scale. A photograph of the thorium spectrum, taken for the 
purpose, shows that the line in question is not truly coincident with the thorium line. 
There accordingly seems to be no sufficient reason why these three lines should not lie 
regarded as part of the scandium spectrum. 

Flutings. 

In addition to the line spectrum, all the photographs, with the exception of those 
of the arc in hydrogen, show a fluted spectrum which is especially strong towards the 
red end, but extends also into the green and blue-green. Several of these flutings 
have previously been noted in the spark spectrum by THALEN, who regarded them as 
being probably due to the oxide of scandium and not to the metal itself. The complete 
disappearance of the flutings when the arc is passed in hydrogen tends to confirm 
THALEN'S view that they originate in the oxide, but no further research on this point 
has yet been undertaken. 

A list of the flutings, all of which fade away towards the red, is given in Table III. 
An attempt has been made to include all the fainter heads as well as the bright ones, 
but some of the heads are rather diffuse and the positions consequently somewhat 
uncertain. 

By far the brightest group of flutings is in the orange-red, beginning at 6017'3, and 
there are fainter groups beginning at G4087 and 5737 '2. There are no flutings in 
the middle green, but three rather feeble flutings, showing structure lines over a long 
range, begin at 4G72'8, 4858'2, and 5133'8. No flutings have been found in the blue 
and violet. 

In the sunspot spectrum there is a hazy line about 6036 '6 which may perhaps 
correspond with the brightest scandium fluting measured as 6036 '48, but as the other 
bright heads cannot certainly be traced (partly on account of Fraunhofer lines) the 
evidence as to the presence of scandium oxide in spots is very slight. 

Comparison with the Solar Spectrum. 

Several important additions to ROWLAND'S identifications of solar lines with 
scandium were made by LOCKYER and BAXANDALL, and other possible coincidences 



AND ITS RELATION TO SOLAR SPECTRA. 55 

were indicated. The intensities of the solar lines, however, were often disproportionate 
to those of corresponding lines in the arc spectrum. 

If we dealt only with the arc spectrum of the element in relation to the sun, the 
selection of lines for representation in the Fraunhofer spectrum would certainly be 
very remarkable. Of two lines in the same part of the spectrum one may be a 
comparatively strong line in the sun, while the other, although at least equally strong 
in the arc, may be weak or missing. For example, the strong line 5672 only occurs 
with intensity in the sun, while 5684, which is much weaker in the arc, appears 
with intensity 1 in the sun. 

These differences, however, become comprehensible when due attention is given to 
the properties of the different lines. The lines of scandium which appear most 
prominently among the Fraunhofer lines are, in fact, the enhanced lines, and within 
the limits of error of estimation they appear with relative intensities which are 
identical with those in the terrestrial spectrum. Lines other than those which are 
enhanced, even though strong lines in the arc, occur only as very faint lines in the 
solar spectrum. 

The coincidences between scandium and solar lines, within the limits of error, are 
numerous, but many of them cannot reasonably be regarded as other than accidental. 
Even a faint solar line may properly be attributed to scandium if coincident with an 
enhanced line of corresponding intensity ; but if the scandium line be not an enhanced 
one, the coincidence can only be accepted as significant when the solar line is faint 
and the scandium line strong. 

The solar lines which may be regarded as true identifications with scandium, in 
accordance with this conclusion, are indicated in Tables IV. and V., one showing 
coincidences with arc-flame lines, and the other with enhanced lines. It will be seen 
that, notwithstanding the occasional confusion caused by lines of other elements, the 
stronger lines of the arc-flame are represented as consistently as can be expected when 
dealing with very faint lines appearing in such a complex spectrum as that of the sun. 
The identification of the enhanced lines, as shown in Table V., is much more definite, 
in consequence of the greater intensities of the corresponding solar lines. 

The result of this comparison is of further interest in relation to the structure of 
the reversing layer. It has already been suggested by JEWELL,* MrrcHELL,t and 
others, that different Fraunhofer lines are produced at different levels, and the 
discussion of the scandium lines tends to support this view. In the case of iron all 
the arc lines, down to the faintest, are well represented by dark lines in the sun, and 
there are no enhanced lines so strofigly shown as the stronger arc lines. With 
scandium it is just the opposite, and the simplest supposition to make is that only a 
small amount of scandium absorption originates at the level which produces the 
majority of the Fraunhofer iron lines. Since direct observations show that enhanced 

* ' Astrophys. Jour.,' vol. 4, p. 138 (1896). 
t 'Astrophys. Jour.,' vol. 22, p. 37 (1905). 



5(5 MR. A. FOWLER ON THE SPECTRUM OF SCANDIUM, 

lines, both of scandium and iron, occur in the upper chromosphere (see p. 59), it seems 
to follow that the greater part of the scandium absorption is produced at a relatively 
hifh level, where the conditions are such as to bring about the comparative isolation 
of the enhanced lines. The same is probably true of strontium and barium, where the 
enhanced lines are strong in the Fraunhofer spectrum, and in the upper chromosphere, 
while the arc lines are feeble or missing. 

It results that Avhile in the case of some elements solar identifications are to be 
based chiefly 011 arc lines, in others it is the enhanced lines which may be expected to 
show the most important coincidences. 

Comparixini with the Simspot Spectrum. 

The previous work of HALE"" and myself t has shown that in the spectra of sunspots 
there is a general tendency for Fraunhofer lines of enhanced metallic origins to be 
weakened, while flame lines are specially selected for strengthening. This difference 
of behaviour is well marked in the case of scandium, as will be seen from Tables IV. 
and V. The data for spots given under " HALE" are derived from the Mount Wilson 
preliminary catalogue, of spot lines, extending from 5009 to 5853,| and from the 
recent more detailed list covering the region 4000 to 4500. The intensities under 
my own name have been derived either from the Mount Wilson photographic map of 
the spot spectrum (4GOO to 7200), or from photographs in the region 3930 to 5800 
which have been kindly placed at my disposal by Mr. MiCHlE SMITH, Director of the 
Kodaikanal Observatory, India. Several lines which have escaped record in the 
published catalogues of spot lines are clearly seen to be affected when special attention 
is directed to them. Some of the lines have also been noted in my own visual 
observations, and in those of CoilTlK and MlTOHELL. 

lleferring first to the enhanced lines of scandium (Table V.), it is evident that in 
the less refrangible parts of the spectrum there is a distinct weakening of these lines 
in spots, while in the region more refrangible than F the evidence as to actual 
weakening is very slight. For the most part there is no definite change of intensity 
of the enhanced lines in the blue end of the spectrum, but it has already been 
recognised that, on account of photospheric light diffused over the spot, or from still 
undetermined causes, the sunspot spectrum as a whole tends to lose its characteristic 
features in the blue and violet, in so far as it has yet been photographically registered. II 
If the difference in the two parts of the spectrum be real, and independent of the 
conditions of observation, it may be that the "phenomenon is related to that found in 

* ' Astrophys. Jour.,' vol. 24, p. 202 (1906). 

t ' Trans. Int. Sol. Union,' vol. 1, p. 228 (1906). 

| ' Astrophys. Jour.,' vol. 23, p. 15 (1906). 

' Astrophys. Jour.,' vol. 27, p. 45 (1908). 

|| HALE, ' Astrophys. Jour.,' vol. 25, p. 90 (1907). 



AND ITS RELATION TO SOLAR SPECTRA. 57 

some of the Wolf-Eayet stars, where the less refrangible lines of hydrogen are bright 
and the more refrangible ones dark.* 

A general comparison of the unenhanced lines with the spot spectrum shows that 
all the more prominent lines are considerably strengthened in passing from the sun to 
the spot. Seeing that the spot spectrum is far more crowded with lines and flutings 
than the solar spectrum, it is not surprising that there are several- apparent coin- 
cidences of spot lines with the fainter lines of scandium, but, with our present 
knowledge, it would be unphilosophical to regard sucli occasional coincidences as 
significant. The only scandium lines which can confidently be regarded as intensified 
in the spot spectrum are, in fact, those which are brightest in the arc-flame spectrum 
previously described. The strongest line of all is 6305 '88, and other prominent lines 
are 6210'90, 5700'40, 5687'05, and 5()72'05; in the blue end, the strengthening of 
arc-flame lines, like the weakening of enhanced lines, is less marked in the photographs 
at present available. 

The principal lines of the arc-flame spectrum, including all the unenhanced lines of 
intensity 6 or more from Table I., are brought together in Table IV. and compared 
with the sun and sunspots. There is a certain amount of confusion with lines of other 
elements in spots, but it may be reasonably concluded that the intensities of the lines 
in spots correspond closely with their intensities in the arc-flame. The line 5514'44 
does not appear in the spot spectrum as might have been expected, but it is at the 
lower limit of intensity, and it would be unwise to conclude from the behaviour of a 
single line that the conditions in spots are very different from those of the arc-flame. 
It may be supposed that while there is a general increase in the scandium flame 
absorption, the increase does not suffice to bring the fainter lines to an intensity 
within the range of observation. 

It is quite certain, therefore, that while the enhanced lines of scandium are 
weakened in spots, the remaining lines are strengthened more or less in proportion to 
their intensities in the arc-flame, at least in the less refrangible parts of the spectrum. 
As the relative intensities of the two sets of lines in spots approximate to those found 
in the arc spectrum, it is possible that there is a descent of scandium vapour from the 
upper region, where the conditions are such as to produce enhanced lines, to a lower 
level where the prevailing conditions approximate to those of the arc. Ixeduced 
temperature of the spot vapour, accompanying this change of level, perhaps provides 
the readiest explanation of the difference between the Fraunhofer and spot spectrum, 
but much further investigation in several directions is necessary before the precise 
nature of the action in spots can be ascertained. 

Comparison with the Chromosphere. 
Two principal sources of data relating to the chromosphere are available for 

* CAMPBELL, ' Ast. and Astrophysics,' vol. 13, p. 457 (1894). 
VOL. CCIX. A, I 



58 MR. A. FOWLER ON THE SPECTRUM OF SCANDIUM, 

comparison with terrestrial spectra: namely, eclipse photographs, and visual obser- 
vations made at ordinary times, the former being especially valuable for the blue end, 
and the latter for the less refrangible parts of the spectrum. Eclipse records are now 
numerous, but completely satisfactory discussions of the lines are not yet possible, 
owing to discordances in the wave-lengths given by different observers, and the 
inadequate resolving powers of most of the instruments which have been employed. 
Nevertheless, since identifications usually depend upon apparent agreement in wave- 
lengths and intensities of several lines of the same substance, there is reasonable 
certainty as to the origins of many of the lines. 

YOUNG'S well-known catalogue of chromospheric lines,* observed without eclipse, 
remains the principal source of information with regard to the less refrangible parts of 
the spectrum, though supplementary observations have been made by MITCHELL,! 
NAGARAJA,^ and myself. Further determinations of the wave-lengths and characters 
of many of the chromospheric lines, however, are urgently needed. YOUNG'S obser- 
vations were mostly made before liowLANo's photographic map of the solar spectrum 
became available, and his subsequent revision was only fragmentary, so that many of 
the wave-lengths cannot be regarded as final. A more complete distinction between 
" high-level" and " low-level" lines is also greatly to be desired. 

A few lines of scandium have been noted by LOCKYER and others in eclipse spectra, 
and a greater number by DYSON, j| who pointed out that the intensities agree well 
with those of the spark. Making due allowance for the lack of highly precise data, 
the general result of the more complete comparison which is now possible is to show 
that it is only the enhanced lines of this element which can be regarded as 
contributing to the chromospheric spectrum. Of the four strongest lines of the arc- 
flame spectrum, G305'88, 5G72D5, 4023'83, and 4020'55, there is no suggestion of a 
chromospheric coincidence except in the case of the last ; DYSON gives a line at 
4020 '50 in his eclipse list, but, as there is no indication of the adjacent similar line at 
4023, the coincidence may be considered accidental, especially as the wave-length 
given by EVERSHED^! is 4020 '3. 

A complete list of the enhanced lines of scandium is given in Table V., which also 
shows the corresponding solar and chromospheric lines. For the region more 
refrangible than 4670, the latter have been taken from DYSON'S tables, Avhile the less 
refrangible lines, with their " frequencies" and brightnesses, are from YOUNG'S 
catalogue. All the brighter enhanced lines are obviously present in the chromo- 
sphere, but the fainter ones, as might be expected, have not yet been recorded. 

* SCHEINEK'S ' Astronomical Speetroscopy,' FROST'S translation, pp. 184 and 423. 

t ' Astrophys. Jour.,' vol. 24, p. 82 (1906). 

t ' Astrophys. Jour.,' vol. 26, p. 150 (1907). 

' Monthly Not. R.A.S.,' vol. 66, p. 362 (1906). 

|| ' Phil. Trans.,' A, vol. 206, p. 440 (1906). 

H ' Phil. Trans.,' A, vol. 201, p. 487 (1903). 



AND ITS RELATION TO SOLAR SPECTRA. < 59 

"Apart from the interference of other lines, the intensities correspond closely with those 
of the terrestrial spectrum. 

This result is in good accordance with the work of LOCKYEK on eclipse spectra, 
which has shown that enhanced lines in general are specially developed in the 
chromosphere. , My own observations* have further shown that enhanced lines 
appear as " high-level " lines in the chromosphere, while arc lines are mostly restricted 
to the region near the photosphere. In the case of scandium, the enhanced line 5527 
is certainly a high-level line, and 5240, according to my recent observations, is of the 
same type. That the same is true of other enhanced lines in the blue, notably 4247, 
is indicated by the lengths of the corresponding arcs in photographs of eclipses taken 
with the prismatic camera. In YOUNG'S catalogue high frequency may often be taken 
as an indication of high level, since lines of the latter class are brought into view by 
comparatively feeble disturbances, and the lines 5031, 5G58, and 5G84 may be regarded 
as of the high-level class from this evidence. 

It may therefore be concluded that scandium exists in the higher reaches of the 
chromosphere, under conditions specially favourable to the production of enhanced 
lines, while there is no evidence of its presence at lower levels except that afforded by 
the feebly developed arc lines in the Fraunhofer spectrum. 

Summary of Results. 

1. The arc spectrum of scandium consists of two distinct sets of lines, which behave 
very differently in solar spectra. Each set includes both strong and faint lines. 

2. Lines belonging to one set correspond with the enhanced lines of other elements, 
notwithstanding that they appear strongly in the ordinary arc spectrum. 

(ft) These lines are very feeble or missing from the arc-flame spectrum, and are 
strengthened in passing to the arc, the arc in hydrogen, or the spark. 

(b) They occur as relatively strong lines in the Fraunhofer spectrum. 

(c) They are weakened in the sun-spot spectrum. 

(d) They occur as high-level lines in the chromosphere. 

3. The remaining lines show a great contrast when compared with the first group. 

(a) They are relatively strong lines in the arc-flame. 

(&) They are very feebly represented in the Fraunhofer spectrum. 

(c) The stronger lines are prominent in sun-spot spectra. 

(d) They have not been recorded in the spectrum of the chromosphere. 

4. The special development of the enhanced lines in the Fraunhofer spectrum, 
together with their presence in the upper chromosphere, indicates that the greater 

* ' Monthly Not. R.A.S.,' vol. 66, p. 362 (1906). 
I 2 



60 



ME. A. FOWLER ON THE SPECTRUM OP SCANDIUM, 



part of the scandium absorption in the solar spectrum originates at a higher level 
than that at which the greater part of the iron absorption is produced. 

5. The discussion of scandium lines indicates that while in the case of some elements 
solar identifications are to be based chiefly on arc lines, in others it is the enhanced 
lines which may be expected to show the most important coincidences. 

6. The flutings which occur in the arc and arc-flame spectra do not appear when 
the arc is passed in an atmosphere of hydrogen. As suggested by THALEN, they are 
probably due to oxide of scandium. 

In concluding this paper the author is anxious to express his great indebtedness to 
Sir WILLIAM CJIOOKES, without whose aid in providing purified scandia the greater 
part of the investigation would not have been possible. Valuable assistance in taking 
the photographs, and in checking some of the determinations of wave-lengths, has also 
been rendered by Miss L. ALUOCK, A.ll.C.S., B.Sc., H. SHAW, A.K.C.S., and 
A. EAGLE, A.E.C.S. 



TABLE I. Arc Spectrum of Scandium. 



FOWLER. 


LOOKYER 

and BAXANDALL. 


EXNEB 

and HASCIIKK. 




Wave- 


f 


Wave- 


* 


Wave- 


O2 


Remarks. 


length. 


3 
t i 


length. 


C 
CD 

HH 


length. 


g 

1-H 




3933-55 


3 


* 




3933-59 


6 


* Possibly masked by Ca line. 




* 






52-43 


1 


* Photographs rather weak here. 


89-18 









89-18 


1 




96-76 


6 


3996-75 


5 


96-79 


15 


ROWLAND gives Sc in sun at 96 68. 


4014-65 


2p* 4014-66 


3 


4014-68 


G 


* Lines marked " p " are enhanced lines. 


20-55 


9 


20-55 


8 


20-60 


20 


Strong arc-flame line. 


23-40 









23 36 


1 




23-83 


10 


23-88 


8 


23-88 


30 


Strongest line of arc-flame spectrum in blue. 


31-53 


1 






31-51 


2 




34-37 









34-35 


2 




37-00 









36-98 


1 




43-98 


2 






43-97 


2 




46-64 


1 






46-64 


2 




47-96 


4 


47-97 


4-5 


47-98 


10 




50-11 


1 






50-09 


2 




52-00 









52-00 


1 




54-71 


6 


54-68 


3 


54-71 


10 




56-75 


2 






56-72 


3 




67-17 


1 






67-15 


2 




75-13 


1 






75-13 


2 




78-72 


1 






78-70 


2 




82-59 


7 


82-59 


6 


82-60 


15 


Strong arc-flame line. 


86-20 









86-15 


1 








86-67 


2-3 









AND ITS RELATION TO SOLAR SPECTRA. 
TABLE I (continued). 



61 



FOWLER. 


LOCKYER 

and BAXANDALL. 


EXNER 

and HASCHEK. 




Wave- 




& 


Wave- 


& 

'OT 


Wave- 




'tn 


Remarks. 


length. 


a 

2 


length. 


1 


length. 


q 

0> 
45 






e 

> i 




d 
i i 




HH 




4086-81 


1 






4086-80 


3 


La? 


87-29 


2 


4087-26 


1 


87 28 


3 








94-85 


2-3 








95-01 


1 






95-03 


1 








4106-02 


2-3 








4133-18 


3 


33-10 


2 


4133-10 


4 




40-45 


4 


40-42 


2-3 


40-42 


5 








41-78 


1 








52-52 


4 


52-50 


3 


52-51 


8 








62-85 


1 












63-77 


1 








65-37 


4 


65 38 


2-3 


65-39 


8 








71-47 


1-2 








71-93 


2 


71-98 


2-3 


71-92 


2 




4218-41 









4218-43 


1 




19-90 









19-90 


1 




22-07 



















4224-32 


1 








25-78 


1 






25-76 


1 




32-09 


2 






32-13 


1 




33-80 


2 






33-83 


2 




37-94 









37 96 


1 




38-25 


3 


38-25 


2 


38-21 


3 




39-74 









39-72 


1 




46-30 









46-27 


1 




47-00 


lOp 


47-00 


10 


47-02 


50 


Strongest enhanced line in blue. 










51-22 


1 




59-86 















83-74 


J 






83-71 


1 




86-73 









86-71 


1 


Er? 


94-94 


4p 


94-91 


4-5 


94-94 


5 




4305-88 4p 


4305-83 


4-5 


4305-89 


8 




14-25 


?P 


14-25 


9 


14-31 


30 


] 


20-91 


7? 


20-90 


9 


20-98 


20 


> Strong enhanced triplet. 


25-15 


6p 


25-15 


8 


25-22 


20 


\ 


48-66 















54-78 


4p 


54-74 


3-4 


54-79 


3 




58-85 


1 






58-85 


1 




59-23 


1 






59-25 


1 




59-83 















65-11 


1 












74-68 


8p 


74-65 


8 


74-69 


20 


Strong enhanced line. 


75-34 









75-32 


1 




81-43 


1 












84-97 


3p 


84-99 


4 


84-98 


3 




89-75 








89-76 


1 




4400-56 


8p 


4400-56 


8 


4400-63 


20 


Strong enhanced line. 


15-72 


7p 


15-72 


7 


15-78 


20 


ii 


20-83 


IP 


20-82 


1-2 


20-84 


1 


29-08 
















G2 



MR. A. FOWLER ON THE SPECTRUM OF SCANDIUM, 
TABLE I. (continued). 



FOWLER. 


LOCKYEK 

and BAXANDALL. 


EXNER 

and HASCHEK. 




Wave- 


t>a 
43 
i I 

m 


Wave- 


j>> 
*i 


Wave- 


Jg- 

w 


Ticiniirks 




length. 


q 

<D 

-i-> 


length. 


1 


length. 


0) 
-*-t 






c 

i i 




I-H 




h^ 




4431-53 


IP 


4431-50 


2-3 


4431-52 


2 




4542-76 


i 






4542-74 


1 




44 88 


2 






44-8G 


1 




57 42 


2 






57-45 


1 






4503-40 


2 








74-20 


o 


74-20 


2 




79-15 


1 








4G04-94 


1 




4G04 88 


1 




09-71 













10-10 















10-59 












70-59 Op 


4070-59 


7 


70 59 


5 




80 OS 2 










.; 


82-10 












4707-10 2 










J 


09-51 2 






4709-53 


1 




11-90. 















14-03 ' 1 










14-52 1 








Ce? 


10-44 


1 












17-21 















19-48 


1 












20 95 













28-95 


9 






29-00 


1 


29-39 


5 i 4729-39 3 


29-43 


2 


32 40 


1 








34 28 


5 34-31 


3-4 


31-31 


3 


35-27 


1 








37-82 


G 


37 88 


4 


37-80 


3 


41-20 


7 


41-24 


5 


41-23 


4 


43-98 


8 


44-04 


G 


44-01 


5 


40-32 


1 








. 


49-15 


1 






(Record 


ends.) 










THALEN (spark).* 


53-35 


G 






4753-8 


1 




59 1 1 


1 












03-25 


3 












71-00 


1 












79-53 


G 










: 


83-09 















84-46 















91-69 


2 












93-14 



















4820-52 


2-3 









* Corrected to ROWLAND'S scale. 



AND ITS RELATION TO SOLAR SPECTRA. 



63 



TABLE I. (continued). 



FOWLER. 


LOCKYER 

and BAXANDALL. 


THALEN (spark). 


Remarks. 


Wave- 
length. 




*OQ 



43 

a 

i i 


Wave- 
length. 


Intensity. 


Wave- 
length. 


Intensity. 


4821-65 















27-47 


4 






4827-8 


1 




33-85 


4 






33-8 


1 








4837-27 


2-3 








39-63 


4 






38-8 


1 




40-62 















41-00 









* 






47-84 


3 






I 




52-86 


4 










59-35 













64-95 


1 










75-50 













78-36 


2 








NotCa 78-31 or Fe 78-41. 


80-90 


1 










90-55 


1 










93-15 


1 












4906-88 


2 












09-89 


3 






4909-5 


1 




23-00 


2 






22-5 


1 




34-39 


1 










NotBii 34-21. 


35-95 


1 










Yb? 






4937-29 


2-3 








41-49 


9 










- 


51-46 
54-22 


I 


54-12 


1-2 


54-5 


1 


Ei- ? 


73-82 


3 






73-9 


1 




80-50 


4 


80-49 


1 


80-4 


1 




83-59 


2 
















87-26 


1-2 








92-07 


4 


92-06 


1-2 


91-8 


1 




95-18 


1 
















5009-68 


2 








5014-32 


1 












18-59 


2 












20-30 


2 












21-67 
31-20 
32-88 


2 
6p 


31-20 


8 


5031-1 


10 


Strong enhanced lino. 


64-50 


3 


64-35 


2 


64-1 


2 




68-98 


1 












70-39 


4 


70-34 


3-4 


70-6 


4 




75-99 


3 


75-85 


1-2 


76-1 


1 








79-79 


1 








80-26 















81-75 
83-88 
85-71 


8 
7 
5 


81-68 
83-77 
85-64 


6 
5 
4 


81-6 
83-6 - 
85-6 


6 
5 

4 


> Strong arc-flame lines. 


87-17 
90-07 


'{ 

3 


87-06 
87-18 
89-95 


3 

2 

2 


| 87-0 
90-1 


5 
1 





64 



ME. A. FOWLEE ON THE SPECTEUM OF SCANDIUM, 
TABLE I. (continued). 



FOWLER. 


LOCKYER 

and BAXANDALL. 


TIIALEN (spark). 




Wave- 


|j> 

CO 


Wave- 


& 

VI 


Wave- 


> 

IB 


Eemarks. 


length. 


(D 
3 


length. 


C 

S 

43 


length. 


C 
m 

.) 






HH 




C 
HH 




C 
II 




5092-54 















96-90 3 


5096-81 


2 5097-0 


I 




99-38 4 


99 28 


3-4 99-1 


4 




5101-26 3 


5101-21 


2 5101-1 


1 








04-43 


1 










05-60 


2-3 






09-20 2 


09-09 


1 









10-85 


<1 






13-00 2 


12-87 


1 






16-86 


3 


16-73 


2 17-6 


2 








21-60 


1 










31-14 


<1 










47-08 













48-28 


2 






5210-68 


5 




5210-8 


2 




11-48 













19-06- 







I 
1 






19-75 


5 




19-3 


o 




39 99 


5p 


5239-99 5-6 39-8 


8 


Strong enhanced line. 


58-49 


5 


58-46 2-3 58-3 


4 








69-65 1-2 






85-15 


1 






85-90 5 85-88 2 85-5 


4 




5302-12 2 






5307-83 1 








14-91 1 












15-77 1 












18-52 2p 


18-41 


o 


5318-3 


o 




23-26 












23-94 














25-14 


2 












28-05 


1 








31-98 


1 












34-43 










Ybl 


39-58 2 






40-0 


1 




41-21 2 






41-0 


1 




43-13 2 






42-5 


1 




49-47 5 


49-32 3 


49-5 


6 




49-91 2 










- 


50 44 1 












56-26 6 


56-14 


3-4 


56-0 


6 




57-38 



















58-69 


2-3 








75-55 


5 






75-6 


4 


Not Th. 






89-89 


1-2 








92-30 


6 


92-12 


3 


92-5 


.6 




5416-43 


o 












25-80 


3 












29-62 


3 












33-43 


4 













AND ITS KELATION TO SOLAR SPECTRA. 
TABLE I. (continued). 



65 



FOWLER. 


LOCKYER 

and BAXANDALL. 


TIIAL&N (spark). 




Wave- 




en 


Wave- 


& 
B 


Wave- 




tn 


Remarks. 


length. 


a 
8 


length. 


| 

m 

+3 


length. 


a 

<D 
-t^ 






a 

hH 




1 t 




a 
> < 




5438-54 


1 












39-26 


2 












42-84 


3 












46-37 5 






5446-5 


4 




47-GG 















51-58 


4 






52-0 


1 




55-51 


2 












65-40 


1 












68-64 


4 












72-42 


4 












74-92 


1 
















5478-66 


2 








82-20 6 82-18 


4 


82-1 


6 


84-83 6 


84-81 


3-4 


85-1 


6 




5514-44 6 


5514-40 


4 


5514-6 


6 




20-73 


7 


20-70 


4-5 


20-7 


6 


27-03 


lOp 


27-03 


10 


27-2 


12 


Strongest enhanced line in green. 


36-60 


2 










41-28 


4 












46-63 


1 












49-90 















50-G4 















52-05 


1 












53-84 


2 












61-34 















65-06 


3 






65-2 


2 




71-48 















79-96 















91-58 


3 


91-44 


2 


91-7 


2 




93-60 


2 












5604-40 


2 












10-33 


1 












24-08 


2 












31-24 


1 












35-10 













Not carbon. 


41-21 


4p 






5641-2 


6 




46-60 


1 












'47-78 















49-80 


2 












58-10 


7p 


5658-10 


7 


57-7 


8 


Strong enhanced line. 


58-56 


2p 


58-56 


3-4 








61-86 















67-40 


3p 


67-40 


3-4 


67-0 


4 




69-28 
72-05 


4p 
10 


69-25 
72-05 


4 
9 


68-8 
72-3 


4 

8 


Strong arc-flame line. 


80-38 















84-43 
87-05 


5p 
9 


84-44 
87-07 


4 

8 


84-5 
87-3 


4 

8 


Strong arc-flame line. 


91-55 















5700-40 


8 


5700-38 


7 


5700-8 


8 


Strong arc-flame line. 



VOL. CCIX. A. 



66 



MR. A. FOWLEE ON THE SPECTRUM OF SCANDIUM, 
TABLE I. (continued). 



FOWLER. 


LOCKYER 

and BAXANDALL. 


THALN (spark). 


T~> 1 


Wave- 


43 

'w 


Wave- 


CQ 


Wave- 


"02 


Remarks. 


length. 


<u 


length. 


1 


length. 


<O 


* 




a 

I-H 




fl 
I-H 




I-H 




5708-85 
11-97 


5 
8 


5711-98 


6 


5708-8 
11-8 


4 
4 


Strong arc-flame line. 


17-51 


5 17-54 


3 17-3 


4 




21-20 


(Record 


ends 








24-30 5 


here. 


) 


24-8 


4 




35-40 












39-53 












41-56 1 












5894-83 2 












5919-21 












31-35 2 












40-70 2 












52-42 


3 












61-65 . 


3 












68-44 


4 












69-37 


4 












88-60 


4 












6021-92 













26-36 


3 












49-02 


1 












6146-50 


3 












93-94 


3 












98-68 


2 












6210-90 


7 






6211-0 


8 


Strong arc-flame line. 


39-95 


7 






39-1 


6 


!) 1) 


45-85 


4p 






47-1 


6 


Strongest enhanced line in red. 


50-16 


3 












59-15 


6 






59-1 


2 




62-48 


3 












73-37 















76-47 


3 












79-95 


3p 






80-1 


2 




84-66 


3 










Probably double. 


93-24 


2 












98-00 















6300-85 


lp 












05 88 


10 






6305-1 


10 


Strongest arc-flame line. 


10-15 


2P 












21-06 


2p 












22-96 















45-04 


1 












79-02 


6 












6413-54 


6 












48-42 


1 












86-56 















95-53 


1 












6525-84 


3 












58-28 


3 




1 










AND ITS RELATION TO SOLAR SPECTRA. 



TABLE II. Impurity Lines omitted from Table I. 



Wave-length. 


Intensity. 


Probable origin. 


Wave-length. 


Intensity. 


Probable origin. 


3988-10 


00 


Yb 


4306-87 


00 


Ce 


4077-52 





Y 


4309-81 





y 


4143-01 





Y 


4352-30 





Sa 


4205-20 





Eu 


4364-82 





Ce 


4222-77 


00 


Co 


4375-10 





Y 


4231-83 





U, Zr 


4382-03 





Th 


4235-49 





Mn 


4391-30 





Th 


4248-82 





Ce 


4391-85 





Ce 


4270-90 





Co 


4398-17 


o 


Y 


4280-09 





Sa 


4863-36 





Th 


4282-25 





Th 


4883-86 


2 


Y 


4290-12 





Ce 


4920-00 





Th 


4296-89 





Ce 


5402-94 





Y 


4306-46 


00 


Gd 


5477-86 





Yb 



TABLE III. Flutings occurring in the Arc Spectrum of Scandium Oxide. 
(All fade away towards the red.) 



FOWLER. 


THALKX.* 








1?i 'in ') rice: 


Wave-length. 


Intensity. 


Wave-length. 


Intensity. 


Vly 1 1 Icll lYCSt 


4672-85 
4707-10 


3 

2 






Head of blue fluting 1 s j 4g50 
Probable sub-head j 


4858-25 


4 






Head of blue-green fluting "1 Structure traced to 


4893-15 


2 






Sub-head ] "'000. 


5133-86 
5171-30 


2 
1 






Head of green fluting 1 Structuro tm , e(1 t(J 5 . m 
Sub-head j 


5737-20 


2 


5737-5 




Beginning of yellow group. 


5761-35 


1 








5764-70 


2 








5773-10 
5775-55 


3 
3 


| 5773-0 






5797-75 


2 








5801-70 


2 


5802-4 




Wide head line. 


5810-15 
5811-82 


3 
3 


| 5810-0 






5836-75 


2 








5839-90 


2 


5843-0 




Wide head line. 


5848-00 
5849-40 


3 
3 


| 5849-5 






5876-95 


1 









* Corrected to ROWLAND'S scale. 
K 2 



MR. A. FOWLER ON THE SPECTRUM OF SCANDIUM, 
TABLE III. (continued). 



FOWLER. 


THALEN.* 


Remarks. 


Wave-length. 


Intensity. 


Wave-length. 


Intensity. 


5878-15 


2 


5878-0 




Wide head line. 


5887-90 


3 


5887-5 







5918-30 


3 


5919-0 




j 


5928-20 


3 








5959 30 1 






Wide head line. 


5968-90 2 






Confused with adjacent So lines in some photos. 


6002-58 1 
















6017-32 4 


6017-0 


4 


Beginning of orange group. 


6036-48 10 


6038-0 


10 




6055-40 2 








6064-54 


9 


6065-1 


8 




6072-90 


8 


6072-6 


8 




6079-60 8 


6080-1 10 




6092-70 1 








6102-07 


6 


6101-5 


6 




6110-17 


5 






6116-31 


6 


6115-9 


8 




6140-60 


5 


6141-1 


4 


Wide head line. A rather uncertain. 


6148-93 


3 


6146-1 


2 




6154-27 


4 


6154-1 


6 


Wide head line. 


6180-71 


3 






) 


6188-35 


2 








6193-20 


4 


6193-4 2 ! Wide head line. 


6220-55 


3 








6229-70 


>> 








6233-30 


.) 








6408-7 2 






Beginning of red group. 


6420-2 1 








6437-4 1 








6446-8 2 






6458-2 


1-2 








6477-0 


1-2 









6485-8 


3 








6496-5 


1 








6517-8 


1 








6526-1 


2 








6535-7 


2 








6567-3 


1 








6576-2 


1 









* Corrected to ROWLAND'S scale. 



AND ITS RELATION TO SOLAR SPECTRA. 



fi9 



TABLE IV. Principal Arc-Flame Lines of Scandium compared with Sun 

and Suuspots. 



Sc arc flame. 


Sun (ROWLAND). 


Sunspots. 




Wave- 
length. 


I 


Wave-length 
and origin. 


"co 

I 


HALE. 


FOWLER. 


Remarks. 




a 




c 






















3996-76 


6 


-96-75* 


00 




* ROWLAND attributes 96-68 (00) 










to Sc. 


4020-55 


9 


Sc 20-55 


1 


( + Fe) 3 


* Fe 20-64 strengthened on violet 












side. 


4023-83 


10 


Sc 23-83 


2 


3 3-4 


4054-71 


6 


Sc 54-71 


00 


* 


2 * Close double with Zr 54-59(0). 












Strengthened on red side. 






fSc-1 








4082-59 


7 


<^ Fe U2-59 


3 


4 


4 Compound line in sun and spot. 






ITiJ 








4737-82 


G 


Fe? 37-82 


1 




2-3* * Probably not wholly Sc. 


4741-20 


7 


Fe? 41-26 


1 




2-3* * 


4743-98 


8 


-44-01 


000 




1 


4753-35 


C 











4779-53 


6 






* Fe 79 -63 strengthened on violet 












side. 


5081-75 


8 


-81-76 


000 00 







5083-88 


7 


-83-88 


000 00 







5087-17 


7 






* 


* Ti <s7-24 strengthened on violet 












side. 


5356-26 


6 


-56-27 


000 00 





5392-30 


6 









5482-20 


6 


-82-20 


0000 


1-2* * Combined with Ti 82 -08. 


5484-83 


6 


-84-85 


000 00-0 





5514-44 


6 


-14-43 


0000 






5520-73 7 -20-73 


00 1 


1 




5672-05 10 


Sc 72-05 





2 


2 




5687-05 


9 


-87-06 


000 


1-2 


1-2 




5700-40 


8 


-00-40 


00 


2-3* 


2-3* 


* H gives Cu? 00-51 as spot line, 














but Sc lino is included and is the 














more affected of the pair. 


5711-97 


8 








* 


* Fe 12-10 strengthened on violet 














side. 


6210-90 


7 


-10-90 


00 




4 




6239-95 


7 


-39-98 


0000 




2* 


* Partly masked by band lines. 


6259-15 


6 


-59-14 


0000 




2 




6305-88 


10 


-05-88 


0000 




6 




6379-02 


6 








2-3 i Falls on band of calcium hydride in 












spot. 


6413-54 


6 








2 





70 THE SPECTRUM OF SCANDIUM, AND ITS EELATION TO SOLAR SPECTRA. 





M 

O 


s- s 1 




e 


-g ? 1 Is "' 






'S S? o "3 o 




**~*v O 

Cd * 3 


"m S. " 




w 


" " "SS 2 




3 


e o c S -s 




** r^-J 


'43-^ * ~ 




O ^ 


H SH g _(J 




h-H 1 -^ 


"3 3 . a '^ ^ 










J 


^^ g rp r~- S o 




-H O 













& 


^ (N <=>?? 




>H "?* 


. _>. o co ^rs s 


t/j 


-? "' 


(M^tOjsj o f^S e 
"2 o '"K 3 ,3 o 








eg 
S 


S5 ^^ 


" M - iJ^oSo^"'^^ 





o5 cj r< ^, -4- ^ 
_, j_, jg* ^i 
o o ^^ oo o d 

" -Cl rl 3 O 

-55 a o, ^;> -c 

*Tn M W *^ TJ 

*P o o .^rz >> o 


Wrs *M - ^ , o 

C W^c^^Q i 1 

^ ^ g 5 S a '^- rQ ^ o i 




c3 w C M ^O C 


^ J PpH G^ t3O2^D"o | I' 




- ^ P. S 

S ft> ^ f-J rl i-^ 1 "^ 

^ o 'w "S ^T "8) 


" | -a g S .S -o ^~ 






rt i~T a E^ Ji* 1^3 o " C ^ "- 1 




J"CC -C <D^ 


O j C ^ C "^^ **1 ^ _ri 




G ^ ~ o w "J^3 ^ 


V s :! -11 i s^ il'1 




i ~3i.il n c; r z: u?r^ -^.ct-. 

^~ *~rt . ^- ^J -4-3 ^~ JT 

3 fl 5 ^ r^ 1 ^ tJDsSji- 

11 1 1 -s^ s|l 

|S g | ^ cocgi 


S " "S a w >,.& >> ~ oo >, a> -c 
| $ |||t- f -2 ?! 
.Sf .5P>,c5 c 2 o ~ o 




0*00 ** ** 


* ** **## *** 






* 

^ CO<M O i ICO i i N CO 


^IISUOIHT 


* 

r-(Or-lC7tM^r-t It CC (M C^l 


m 


CJ 




^<co o i 100 i i <M in 


t-t 






O 




w 


A^ 


t O CO i i OO 1C t i --t t O iO fe 




2 cc 


1 O C 1 ! CO CO Oi C-1 tO r i tOCO -^ g 


5 * * * * * 




^ I >O if? -^ O 1O 'f O O O O O 


pj CO O O CD i i I !M 1- 


KH, 






^ "i 
> 


^-oIl^-CJl^OlK^ OO O 


i co-? c<i --fin COCDCC 
> Of>i in oto COCDCO 


c 


^ r% r. 


03 om m min inmin 






P= 




H 


* ^ 




^ vfyisiio^iii 


s cSdriridrid* c s =5 * - 






o 


'o o 


03 rt 






3 H 




(M 


H 'AQISHOIUT 


III 


1 


w 


CO CO (M O 


i ( 


Ajsuoiiq 


lC)O<M<MCOCO'^t i CC O CO CO O O (M 

o 


CO - i O CO I-H <M O O i ' ' i iOO O 

o o o 






o 


1? 
rg 


COOCiGOG^lCit-Ht OC^lOt OOOO 


OOCOCO i O CO t CD C-1 COlOO t- 
<M C^ id O G^l i ' lO CO C-l -^ OO Oi Oi O 


StiD 
M p-i 

02 g 


^t -f | iO'^OO-i''^f-^OOOt 'O 


i i O OO t^- I-H CO OO t Oi Tf 1O O O ^ i * 

CO CO i I CM -^HlOlO^O^OOO *** t O <M 


O T 


oof-i|ooo[clo| 1 1 1 


1 1 1 1 t ^H 1 1 1 1 III 1 


/v* O 

M ; 


Ca^CCM tfmitfl Q O2 


| 


08 


fe 




^ 


t 




>jf u 


<NO-*-*t-t-tOTjeoOOt-r-ipHo 


CO *O <?1 O "^ t (M CO "^ *O "^ ^f I-H M (M 


I'M' 






.2 H 




co in o m m D 


ri fe ^TI 


tOOOiOOC.lS2SSSSooSS 


C^CiiOO (M ^H i5 ^ <M T? OOO^GOr O 


gO 60 


^^?So^SSintiooo2coS 


r lOiOOt < i 00 OO t* C5 ^ lOOOOi-H 


"* ^ p^ QJ 


O> C^l C 1 ! CO CO CO CO CO CO CO "^ *^ "*f* ^+* CO 


^5 C*l CO lO CO tO CO CO CO tO C 1 '! C"! CO CO CO 




^^^^^^^^^^^^H^^^. 


IO IQ O lO lO O IQ lO lO O CO CO CO CO CO 



IV. On the Nature of the Streamers in the Electric Spark. 
By S. R. MILNER, D.Sc. (Lond.), Lecturer in Physics in the University of Sheffield. 

Communicated by Prof. W. M. HICKS, F.R.S. 

Keceived February 10, Read March 5, 1908. 
[PLATES 2-4.] 

WHEN the oscillating electric spark is examined in a rapidly rotating mirror, the 
successive oscillations render themselves evident in the image as a series of luminous 
curved streamers which emanate from the poles and extend towards the centre of the 
spark gap. These streamers were first observed by FEDDERSEN* in 18G2, but the 
work of SCHUSTER and HEMSALECH! in 1900 may be said to have opened up a new 
era in the subject. These workers threw the image of the spark on the slit of a 
spectroscope, and photographed the resulting spectrum on a film which was maintained 
in rapid rotation in a direction at right angles to that of the incident light. In their 
photographs they found that the air lines extended straight across from pole to pole, 
but that the metal lines were represented by curved bands drawn out in the centre of 
the spark gap. There is a close relation between these bands and the streamers seen 
in the unanalysed inductive spark: SCHUSTER and HEMSALECH carried out their 
experiments with the smallest possible inductance in series with the spark, and thus 
made the period of the oscillations so small that the drawing out on the film was 
insufficient to separate the individual oscillations from each other. Thus their curved 
lines represent a composite structure, consisting of all the streamers due to the 
successive oscillations superposed on each other. It follows from their results that 
the light of the streamers in the spark is entirely produced by the glowing of the 
metallic vapour of the electrodes, and that, while the luminosity of the air is practically 
instantaneous in its occurrence, that due to the metal vapour occurs in the centre 6T 
the spark gap an appreciable time later than near the poles. 

The actual process which goes on in the spark and gives rise to this delay in the 
arrival of the metallic vapour at the centre of the gap is not yet thoroughly 
understood. SCHUSTER and HEMSALECH make the natural supposition that it is due 
to the fact that the metal of the electrode is vaporised and rendered incandescent by 
the heat of the spark, and that the vapour takes an appreciable time to diffuse from 

* 'Pogg. Ann.,' vol. 116, p. 132 (1862). 
t ' Phil. Trans.,' A, vol. 193, p. 189 (1900). 
VOL. CCIX. A 444. 16.11.08 



72 DK. S. E. MILNER ON THE NATURE OF 

the electrodes to the centre of the gap. The exception which has been taken to this 
view has arisen in part from the difficulty of observing the Doppler effect on the 
metallic lines which should be a concomitant of the diffusion of the vapour from the 
poles,* and in part from the extraordinary results which the authors themselves 
obtained in some metals for the velocity of the diffusion corresponding to the different 
lines. In the case of bismuth and, in a less degree, of cadmium the different metallic 
lines could be divided into groups of different curvatures which indicated different 
velocities of diffusion towards the centre of the gap. As regards the former matter, 
there does not seem to be involved any real difficulty to the explanation, as 
Dr. SCHUSTER has himself recently shown, f The curious effect of the different 
curvatures of the lines of the same element has, however, always remained more or 
less of a difficulty in the way of a complete acceptance of their view. SCHUSTER and 
HEMSALECH themselves refer to the possibility in the case of bismuth that the metal 
may be a compound, and that the two kinds of molecules give rise to the differently 
curved lines. Other explanations* have been made by different writers, but it cannot 
be said that any explanation adequately supported by experiment has been forth- 
coming. In view of this incompleteness in our knowledge of the constitution of the 
streamers it seemed to me that further observations with a rotating mirror would 
possibly be of value, and the investigations recorded below succeed, I think, in 
throwing a clearer light on the nature of the streamers, and on certain other 
phenomena which are characteristic of the spark. 

In the first experiments which were made the light of the spark was not submitted 
to spectral analysis, but was observed as simply drawn out by the rotating mirror. 
While they were only of a preliminary nature they nevertheless gave some interesting 
results which merit a short description. The sparks were obtained by the discharge 
of a battery of 12 Ley den jars which were charged by an induction coil worked by a 
mercury platinum break. By means of a length of insulated copper wire, wound on a 
cylindrical rod and containing terminals along its length, varying amounts of 
inductance could be inserted in the discharging circuit. The poles between which the 
spark took place were pointed metal rods, held in corks and placed, one vertically 
above the other, in a small box with a single opening which cut off all light from the 
r^)om except that by which the spark was examined. At its focal distance away from 
the spark was placed a large lens throwing the light in a parallel beam on to the 
rotating mirror, by which it was reflected on to the lens of an ordinary half-plate 
camera. The mirror was fixed on the axle of a gear-wheel arrangement, and could be 
rotated about a vertical axis by a motor at speeds up to about 150 rotations per second. 
The induction coil gave one or two sparks every second, of which perhaps one in every 
dozen was reflected into the camera. By looking through the back of the plate in the 

* HULL, ' Astrophysical Journal,' vol. 25, p. 1 (1907). 

t ' Astrophysical Journal,' vol. 25, p. 277 (1907). 

J Of. J. J. THOMSON, ' Conduction of Electricity through Gases,' p. 397 ; p. 520 in 2nd edition (1906). 



THE STREAMERS IN THE ELECTRIC SPARK. 73 

camera while keeping control of the shutter, it was possible to expose for the few 
seconds required to just catch one or two good images on the plate and yet avoid the 
confusion of many overlapping ones. 

The appearance of the drawn-out spark obtained with a small inductance 
(O'OOOl henry) in circuit is shown in the photograph, fig. 1, Plate 2. We see the 
initial air discharge extending straight across from pole to pole, and succeeding it the 
streamers, starting from the poles and crossing each other in blurred masses in the 
centre of the spark gap. The streamer corresponding to each oscillation is observed 
to be much more prominent at one pole than at the other ; this fact was noted both 
by FEDDERSEN and by SCHUSTER and HEMSALECH, but they were unable to determine 
from their photographs whether it was the positive or the negative pole from which 
the main streamer started. SCHENCK,* who subsequently investigated the spark by 
means of a rotating mirror, observed that the streamers came from the cathode in each 
case. HEMSALECH,! in a later research on the spark in which he separated the, 
oscillations by blowing a current of air across them, found that it was from the positive 
pole that the streamers emanated. In each of my experiments the direction of the 
first discharge of the spark was determined by noting the direction of the discharge 
produced by the induction coil through an X-ray tube ; the nature of the poles in the 
subsequent oscillations could then be easily ascertained by counting from the first 
discharge. In all the photographs, which comprise different metals, inductances, and 
capacities, and also different lines of the same element, I find, in agreement with 
SCHENCK, that in every case it is the cathode from which the stronger streamer 
emanates. There is, however, in all cases a tendency to a discharge from the anode. 
In the softer metals, such as magnesium and lead, this becomes very pronounced and 
nearly as strong as the cathode discharge. (See fig. 2, Plate 2, a spark between 
magnesium terminals.) With regard to HEMSALECH'S result it is to be observed that 
he worked with much more inductance in the circuit than either SCHENCK or myself, 
and it is possible that his different result is diie to the conditions in his experiments 
being more analogous to those obtaining in the arc than in the ordinary spark. 

An interesting point was noticed in several of the photographs which throws a clear 
light on the nature of the streamers. This is illustrated in figs. 3,4, and 5 (Plate 2). 
These photographs show oscillations of some of the streamers which represent backward 
and forward motions of the vapour forming them which are exactly synchronous with 
the oscillations of the spark itself.j 

* ' Astrophysical Journal,' vol. 14, p. 116 (1901). 

t 'Comptes Rendus,' vol. 142, p. 1511 (1906). 

| The sparks reproduced in figs. 3, 4, and 5 were taken in a magnetic field as described on p. 75. 
The magnetic field, while having nothing to do with the production of these oscillations, generally makes 
them more prominent, as the irregular course of the streamers produced by the field, which is referred 
to on p. 75, prevents them overlapping in the centre of the spark gap. It thus happened that these 
negatives showed the oscillations best, but the backward motion of the vapour is shown by many of my 
negatives of sparks without a field. 

VOL. CCIX. A, L 



74 DR. S. R. MILNER ON THE NATURE OF 

In their work on the inductionless spark, Messrs. SCHUSTER and HEMSALECH have 
observed an effect in the case of cadmium which is apparently somewhat similar to 
the "above. Some of the metallic lines showed a wavy outline, which presumably 
indicated that the vapour had a velocity which alternately decreased and increased as 
it receded from the pole. This led them to suggest in 1900 the possibility that the 
metallic vapour was charged and carried the electric current, but the effect was not 
sufficiently marked in their photographs to enable them to make any definite assertion 
in this respect. SCHENCK later, in 1901,* showed that the streamers could not be the 
actual carriers of the current, as they do not proceed more than a short distance 
across the spark gap before the electrical discharge becomes reversed. 

My photographs are therefore important, as the fact that the luminous vapour 
actually come* hack towards the pole when the electric field of the spark reverses its 
direction forms so much definite evidence that the particles of which it is composed 
must be charged. This suggests that modifications may be called for in our view of 
the nature of the streamers. While one view of their constitution is that they are due 
to purely thermal diffusion and incandescence of the vapour of the electrode metal, 
another one possible is that they are mainly produced by the luminescence of charged 
atoms suddenly torn off from the surface of the electrode, and propelled towards the 
centre of the spark gap by the intense electric field of the spark ; and the photographs 
support the second of these conceptions. This view has the advantage of relieving us 
of the necessity of making any hypothesis as to the temperature of the spark, for it is 
not difficult to imagine that the sudden release from strain which would occur as the 
atoms are torn off from the surface of the metal might give rise to the vibrations 
which correspond to the characteristic metal lines of the spark, apart from any 
thermal incandescence of the vapour. It is clear, however, that the electric force of 
the spark is not by itself capable of tearing off the atoms from the surface of the 
electrode, for the force exists before the spark begins to pass. But when the discharge 
has actually begun the metal surface is being bombarded by the ions, which carry the 
current, and this bombardment also is doubtless an essential factor in the disruption 
of the surface and the production of the luminescence. This view perhaps suggests 
a reason why the streamers are so much more vigorous at the negative than at the 
positive electrodes, if we suppose that the positive ions which carry the current of the 
spark are more efficient in causing disruption of the surface than are the (probably 
smaller) negative ones. Such a result would at any rate be in accord with their other 
known capabilities as regards ionisation. 

Effect of a Magnetic Field ott, the Streamers. 

In order to test these points still further, I made some observations on the effect of 
a magnetic field on the course of the streamers. A strong magnetic field was arranged 
at right angles to the length of the spark, and so that its direction coincided with 

* LOK. at. 



THE STREAMERS IN THE ELECTRIC SPARK. 



75 



that of the line joining the spark to the rotating mirror, and a series of photographs 
was taken with ziuc and with magnesium terminals. If the streamers are charged 
atoms in motion, the theoretical effect to be expected would be that those going up 
should be deflected in one direction and those going down in the opposite one, thus 
producing in the photograph a want of symmetry in the course of the streamers from 
the two electrodes. Such a want of symmetry was indeed found, but the deflections 
were in the opposite directions to those which would be produced by the action of a 
magnetic field on negatively charged atoms. The sparks in figs. 3, 4 and 5 were taken 
in a magnetic field, and they show, in addition to the oscillations already referred to, 
the want of symmetry in the streamers produced by the field. A close inspection 
shows also that it is due to the streamers coming off not from the ends, but from the 
sides of the electrodes. Examination of all the photographs taken 
under these conditions showed that the effect which really takes place, 
although there are occasional irregularities, is this : Suppose the top 
electrode A (in the accompanying diagram) is the cathode, and B the 
anode, for the initial discharge which gives the air lines, and that the 
magnetic field is downwards through the paper. The. line of the first 
discharge lies straight across from the point of B to the point of A, and 
a streamer appears at the point of A. Then, during the back discharge 
when B is the cathode, the streamer starts from the left-hand side of B, 
not its point, but the anode is the point of A. The anode can lie 
distinguished in the photographs as faintly luminous. The next 
streamer starts from the right-hand side of A, the corresponding anode 
for the discharge being the point of B ; and these paths with occasional 
irregularities are adhered to in the subsequent discharges. 

The effect may, I think, be explained without difficulty. In the interval between 
the first and second discharges the column of ions in motion which marks the line 
of the first discharge is moved by the magnetic field to one side of the direct line 
joining the electrodes. In the next discharge the line of maximum electric force is 
directed towards this ionised column, and the streamer starts from the side of the 
electrode in the direction of the maximum electric force. This gives an apparent 
deflection opposite to that which would be looked for as the effect of the magnetic 
field on the streamer itself. It is very possible that the latter exists when the 
streamers are once in motion, but I have not been able to find any decisive evidence 
of it in the photographs ; the effect, if existent, is overlaid by the drawing out of the 
streamers by the mirror. The current itself in the second discharge is, however, 
certainly deflected by the field, the anode being clearly marked at the point of A ; 
thus the ions which carry the current must be deflected by the field along the curved 
path CD. By the time the next discharge occurs the column of ions has been carried 
to the right-hand side of the electrodes, and we get the streamer starting from the 
side of A and the current traversing the deflected path EF. 

L 2 




76 DE. S. R. MILNER ON THE NATURE OF 

This displacement of the streamers by a magnetic field I found could be easily 
observed without using a rotating mirror. Figs. 6, 7 and 8 are photographs of sparks 
taken between the edges of two zinc plates placed at right angles to each other about 
a centimetre apart, fig. 6 without, and figs. 7 and 8 with a magnetic field on, in 
opposite directions in the two cases. In the two latter figures the streamers are 
displaced along the edge of the plate at the bottom of the figure, and the amount of 
drawing out being a little irregular some of them can be seen without overlapping. 
From the upper plate seen end on the streamers come off at the side. By increasing 
the inductance in the sparking circuit the separation of the streamers can be made 
still greater ; with sodium electrodes and large inductance an enormous drawing out 
(several centimetres) of the streamers at the side of the spark can be obtained, and 
the discharge even made to pass in a spiral path between the two electrodes, which is 
evidently due to the action of a magnetic field on moving ions. 

The next point which called for attention was the examination of the streamers in 
the different monochromatic lights corresponding to the metallic lines of the spark. 
The measurements of Messrs. SCHUSTER and HEMSALECH, as has already been 
mentioned, were restricted to the case where no inductance was in circuit with the 
discharge. Under these conditions the period of the oscillations is so extremely 
minute that the streamers corresponding to the individual discharges are all super- 
posed on each other, and the details of the structure of the single streamer are 
completely masked. My first experiments were carried out on similar lines, but with 
inductance inserted in series with the spark. Although they showed some interesting 
features, the streamers corresponding to the various lines were so mixed up by 
superposition on the plate that little detail could be seen. The apparatus was 
therefore modified in the following way : A three-prism Hilger spectroscope had 
the collimator slit and the telescope removed, and the remaining parts were fixed on 
a wooden stand in such a way that, while the light emerging from the last prism face 
came out in a horizontal plane, the plane containing the prisms and the collimator 
was inclined at 45 degrees to the horizontal. The spark, which took the place of the 
removed slit, was turned round in a plane at right angles to the collimator axis until 
it made an angle of 45 degrees with the plane of the spectroscope. The light 
emerging from the prism face in a parallel beam fell upon the rotating mirror with 
its axis vertical, from which it was reflected direct on to the camera lens. By this 
arrangement a series of monochromatic images of the spark was produced en echelon 
on the ground-glass screen of the camera when the mirror was stationary, the images 
being vertical and the dispersion being inclined at an angle of 45 degrees to the 
horizontal on the screen. The rotation of the mirror causes each of these images to 
be drawn out in a horizontal direction ; and we can thus photograph simultaneously, 
without much overlapping, a series of images of the streamers in the same spark 
impressed on the plate by the monochromatic lights of its different metallic lines. 



THE STREAMERS IN THE ELECTRIC SPARK. 77 

When the metal lines are close together a certain amount of overlapping still takes 
place, but it is generally possible to distinguish the streamers due to the stronger 
lines even when this occurs. 

Using the spark itself as the source of light instead of its image thrown on the slit 
of the spectroscope has the advantage not only of simplicity, but also of giving us a 
truer rendering of the course of the streamers. The course of the spark discharge is 
often very variable ; instead of going straight across from pole to pole, the spark 
curves round, and its image is very likely to fall off the slit in the centre of the gap ; 
and with a slit in such cases the resulting photograph will give a false impression ot 
both the velocity and the extent of the streamer. By using the spark itself as the 
source of light, the air lines show the actual path taken by the discharge, and any 
curvature in them can be taken into account in studying the shapes of the streamers. 

With this apparatus, and using the electrical arrangements previously described, 
about a hundred exposures have been made on sparks with different metals, 
inductances, capacities, and spark lengths. From the resulting photographs, of which 
a selection is reproduced to accompany this paper, the behaviour of the different 
lines, as regards the appearance, velocity, duration, &c., of the streamers, could be 
studied at leisure. Descriptive notes on the photographs reproduced are given at 
the end of the paper, and in the following account I shall confine myself to describing 
the general conclusions which follow from the examination and comparison of the 
whole series, referring when necessary to the figures in which the best illustrations 
of them can be seen. 

Durations of Lines. 

The durations can best be studied quantitatively when there is no inductance in 
series with the spark gap beyond that of the connecting wires. The period of the 
oscillations is then extremely small, and the whole spark from an electrical point of 
view is over before the image is appreciably drawn out on the plate. The fact that 
nevertheless the metal lines are always drawn out shows that their vibrations last an 
appreciable time after the stimulus which has excited them has ceased ; this time is, 
moreover, very different for the different lines. 

We may take as an example the magnesium spark, fig. 24 (Plate 3), the luminosity 
of the triplets (5183, 5172, 5167) in the green (nearest the top),* and (3838, 3832, 
3829) in the ultraviolet (both unresolved of course), lasts at' least four tunes as long 
as that of the line A. 4481, which itself has a duration of 16 micro-seconds after the 
actual spark has ceased. The two triplets are prominent arc lines, 4481 is the well- 
known spark line, absent from the arc under ordinary conditions. When a little 
inductance is inserted in the sparking circuit, as in fig. 25, the difference in the duration 
of the lines makes itself evident in another way. With X4481 the streamers are 

* The line has almost disappeared in the reproduction, but in the negative shows as an exact but fainter 
copy of the ultraviolet line at the bottom of the figure. 



78 DE. S. E. MILNEE ON THE NATUEE OF 

clearly separated, giving sharp-cut images, but the streamers corresponding to the 
triplets still overlap and show a confused image with very little detail. Fig. 25 
confirms the observations of SCHENCK,* who, also examining the magnesium spark 
by a rotating mirror, observed that the streamers in it were associated almost entirely 
with the spark line 4481, the arc lines giving only a diffuse luminescence which lasted 
in the centre of the spark gap for some time after the actual discharge had ceased. 
It would be incorrect, however, to infer that the arc lines take no part in the 
production of streamers ; my results show that all the lines of a metal are exactly 
equal in this respect, and that the clearness of the individual streamers is entirely a 
question of the varying durations of the lines. By inserting enough inductance in 
series with the spark, and thus separating the oscillations sufficiently on the screen, 
the streamers corresponding to the arc lines can always be rendered clear. Thus in 
ficr. 26, where the inductance in circuit has been increased, the streamers in the ultra- 
violet triplet are distinctly shown. 

The difference which we have noted in the behaviour of the arc and the spark 
lines of magnesium is characteristic of the whole of the metals examined. In every 
photograph of the inductionless spark the arc lines last from four to six times as long 
as the spai-k lines. With a little inductance inserted the spark lines always give rise 
to sharp- and clear cut streamers, in sharp contrast to those of the arc lines, which 
are diffuse and often overlap, producing a uniform luminosity which lasts some time 
after the oscillations themselves have ceased. The streamers of the arc lines can, 
however, always be rendered evident by inserting sufficient inductance in the circuit. 
The number of oscillations registered on the plate is also generally a little greater for 
the arc than for the spark lines, say about 14 oscillations as against 12. 

A detailed examination of the photographs showed that the spark lines themselves 
are in many spectra divisible into two classes. We may take as an example fig. 14 
(Plate 2) of the bismuth spark. In this figure the three diffuse drawn-out bauds 
represent (counting from the top of the figure) the prominent arc lines 4722, 4122, 
3 596, and the three sets of strongly-marked and clear-cut streamers lasting 
throughout nearly the whole duration of the spark can be identified with the groups 
of spark lines (5208, 5144, 5124), (4340, 4328, 4301, 4259), (3864, 3792, 3757). 
In addition to these the lines 4560 (just below the highest arc band), 3695, and 3613 
(at the bottom of the spark) can be seen. The first streamers of these lines show as 
intense clearly-marked dots extending from the electrode only a short distance towards 
the centre of the spark gap. The next streamers are much fainter, and after two or 
three oscillations only no trace of the lines is visible. I have found lines of this class 
only in the spectra of the metals aluminium, antimony, bismuth, lead, and tin. (It must 
be remembered, however, that only the fairly strong lines of the metals can be observed 
in the? photographs.) They are extremely sensitive to the influence of inductance in 
the spark circuit, and disappear altogether from the spectrum when more than a very 

* Loc. at., p. 129. 



THE STREAMEES IN THE ELECTRIC SPARK. 



79 



small amount is introduced. In the condensed spark without inductance they are 
usually very bright at the start, but their luminosity dies away much more rapidly 
than that of the ordinary spark lines. It will be convenient to speak of them as 
" condensed spark " lines, although it would be premature to suppose that there is 
any absolute distinction between them and the ordinary spark lines. 

Numbers for the durations do not, of course, represent any very definite property 
of the lines, and only have a value in the absence of more exact knowledge. It is, 
however, very striking in most spectra how sharply distinguished in duration the lines 
of the different classes are from each other. In any particular spectrum the lines of 
each class seem to have all practically the same duration, and there is a big step in its 
value to that of the other classes. The durations in many cases vary very little from 
metal to metal, so that it is possible to arrange the metals in groups and to give ;ui 
average value of the duration which applies fairly accurately to each group of metals 
and each class of lines. This is done in the following table : 



Metals. 


Durations (micro-seconds). 


Arc lines. 


Spark lines. 


Condensed spark lines. 


Al, Bi, Pb, Sb, Sn 
Cd, Cu, Hg, Mg, Zn 

Ca, Na 


10.3 
66 
160 


16 
12-5 
38 


8-5 



The actual differences between the classes are likely to be .somewhat greater than 
these numbers would imply, both as a result of the whole of the light of the lines not 
being shown through under-exposure, and also of the fact that the small but constant 
time during which the electrical discharge occurs and all the lines glow equally is 
included in them. 

In connection with this evidence it must be observed that the greater duration 
of lines is not combined with a greater intrinsic brightness at the beginning of the 
discharge ; on the contrary, the intrinsic brightness of the arc lines at the beginning 
of the discharge is usually much less than that of the spark lines, although, since 
their light dies away at a slower rate, they may exceed the latter in brilliancy in the 
photograph of the stationary spark. The difference between the classes is in reality 
one of the magnitude of the logarithmic decrement of the atomic vibrations corre- 
sponding to the lines, the arc lines having a small, and the condensed spark lines a 
very great, decrement. 

Velocity of the Streamers. 

It is not an easy matter to obtain values of the velocity of the streamers which will 
serve as a trustworthy basis in the comparison of different sparks, because the shapes 
of the streamers in the sparks of different metals are often quite different. Compare, 



go DK. S. R. MILNER ON THE NATURE OF 

for instance, the bismuth and the mercury streamers in figs. 14 and 29. The bismuth 
streamers spread out fanwise from a point, while the mercury ones converge to a point 
from a broad base.* The velocities also vary somewhat erratically in different sparks 
with the same metal. Consequently, while numerical values of the velocities are 
given in the notes on the individual photographs, it would be inadvisable to lay very 
much stress on them as representing more than very roughly any absolute values 
characteristic of the metals. They are, however, sufficient to admit some conclusions 
to be drawn from them. It may be observed that these difficulties do not enter into 
the comparison of the velocities of the streamers corresponding to the various lines 
of the same spark, for which the photographs are well adapted. 

In considering the velocities a distinction has to be drawn, as was first pointed out 
by ScHENCK,t between the velocity with which the front of the metallic vapour 
approaches the centre of the spark gap and that of the vapour in the subsequent 
individual streamers. Thus, taking as an example fig. 26, it will be seen that the first 
streamer goes only a little way towards the centre of the gap, and then its velocity 
falls off very rapidly, as is shown by the sudden way in which it curls round and stops 
short. The next streamer goes a little further, and it is not until after two or three 
oscillations that the successive streamers become fairly uniform. The velocity with 
which the front of the metallic vapour approaches the centre of the spark, which is 
that represented by the locus of the extremities of the streamers, is thus very much 
less than that of the streamers in the earlier parts of their course. This effect is 
shown more or less by all the photographs. The probable explanation of it is, I think, 
that the puff of vapour in the first streamer is rapidly stopped by the resistance of the 
air present between the poles. The velocities of the streamers quite close to the 
electrodes are, however, very big, and it is quite possible that they are greater than 
the molecular velocity of the surrounding air. If this is the case, each puff of vapour 
will leave a region of smaller pressure behind it, and into this the vapour of the next 
streamer can be propelled with comparative freedom from friction, and so be propa- 
gated further towards the centre of the gap. 

This behaviour of the streamers makes it necessary also to distinguish between the 
velocity of an individual streamer in the oscillating spark and the velocity of the 
vapour in the spark without self-induction. In the inductionless spark the streamer 
is a composite one formed of a number of superposed true streamers, and unless the 
discharge is absolutely instantaneous and the superposition perfect the velocity 

* In photographs taken without a slit the shape of the streamers will be affected by any spreading out 
sideways which the vapour composing them may undergo as it recedes from the pole. This, and the 
effects of superposition and under exposure which are referred to below, doubtless account for most of the 
differences observed in the shapes of the streamers in the sparks of different metals. In so far as these are 
the causes of the different appearances the measurement of the central line of the streamers will give true 
values of the velocities. 

t ' AstrophysicalJournal,' vol. H, p. 133 (1901). 



THE STKEAMERS IN THE ELECTRIC SPARK. 81 

represented by the locus of the extremities will be different from that of the streamers 
themselves. There is also another reason why the velocity of the vapour in the 
inductionless spark should be less than that of the individual streamers. We have 
already seen (p. 74) reason to believe that the metallic vapour in the streamer is 
electrically charged, and consequently its motion is alternately accelerated and 
retarded by the oscillating electric force of the spark. In the spark with sufficient 
self-induction the streamer can travel as far as the centre of the spark gap 
during the period the accelerating force only is in play ; in the inductionless spark 
the retarding force will come into play when the streamer has proceeded only a 
minute distance from the electrode, and its average velocity throughout its whole 
course will be accordingly diminished. The measurements of the velocities are in 
entire accordance with these considerations. They show that the velocities of the 
vapour for the inductionless spark are consistently only about half as great as those of 
the individual streamers of the same metal in the spark with self-induction. 

Messrs. SCHUSTER and HEMSALECH found as a result of their researches that, 
among the metals they examined, those which possessed the lowest atomic weights 
gave the highest velocities in the spark. My observations do not confirm this 
conclusion for the more extensive list of elements which. I have examined. For 
example, sodium, having the lowest atomic weight, shows the lowest velocity of all the 
metals examined. 

I have examined all my photographs in order to find, if possible, evidence of any 
differences in the velocities which correspond to the different lines of the same metal 
in the spark, but I have not been able to find any in any case. There are occasional 
apparent differences, but they can always be adequately accounted for as the result of 
some portions of the streamers by reason of under-exposure failing to affect the 
photographic plate. 

It is to this cause, I think, that the differences obtained by Messrs. SCHUSTEK and 
HEMSALECH in the velocities of the different lines of bismuth and cadmium must be 
ascribed. It must be remembered in this connection that the intensity of a streamer, 
while it may be very great near the poles, falls off rapidly as the centre of the spark 
gap is approached. Thus the photographed outline of even a single streamer cannot 
accurately coincide with the actual outline of the luminous vapour, for if we go 
sufficiently far out the light can not be enough to affect the plate. This effect may 
indeed be seen in almost every photograph, although in spite of it it is usually 
apparent that the velocities are the same. A more marked effect will, however, be 
produced in the photographs of the spark which has no inductance in circuit with it 
beyond that of the connecting wires. Here, through the minuteness of the periodic 
time of the oscillations, we are dealing with a number of streamers which are very 
nearly (although not exactly) superposed on each other. The resulting image on the 
plate is due to the combined photographic effect of them all. Let us suppose that the 
brightness of one of the single streamers falls off at such a rate that, at a certain 

VOL. CCIX. A M 



82 DR. S. K. MILNER ON THE NATURE OF 

distance from the pole towards the centre of the spark it is too low by itself to affect 
the plate. A short distance to one side of this point the second streamer (itself also 
insufficient to affect the plate) is superposed on it, and the two together will have 
sufficient intensity to produce a photographic effect. The apparent outline of the 
luminous vapour will be thus displaced to one side. A little further out, where the 
individual streamers are still less bright, it will require the combined effect of three 
streamers to affect the plate, and the apparent limit of the vapour will be displaced 
still further to the side of the true edge of the first streamer. Thus the apparent 
velocity of the vapour towards the centre of the spark will over a certain region 
always be less than the actual velocity, and the extent to which it is so will depend on 
several circumstances, of which the rate at which the luminosity of the streamers dies 
away and the period of the oscillations of the spark are two of the chief ones. The 
period of the oscillations is the same for all the lines in the same spark, but the rate 
at which the intensity of the light of the streamers corresponding to the various lines 
dies away is, as we have seen, very different, hence the apparent velocities due to this 
cause would also be different for the different lines. It is necessary, of course, that 
the period of the oscillations should be sufficiently large for the streamers to be 
separated from each other to an appreciable extent, if there is to be produced a 
measurable change in the velocity by means of this effect. That this is the case in 
the measurements of Messrs. SCHUSTER and HEMSALECH is, I think, evident from 
an inspection of their figure 2G of the bismuth spark, where the streamers in the 
lines of short duration are clearly separated in the photograph. Hence it seems 
to me that the effects of varying velocities for the different lines which they 
obtained in their researches may be adequately accounted for in the way described 
above. 

Another point to which attention was paid in the examination of the photographs 
was the possible existence of differences between the anode and the cathode streamers 
in each oscillation. It would be interesting, as bearing on their constitution, if any 
lines were found which were associated with either the anode or the cathode discharge 
to a greater extent than other lines, but a close scrutiny has not revealed the 
existence of any such cases. The only case of any difference in the character of the 
anode and cathode streamers which I have found is that shown in the mercury spark 
of fig. 29, and the difference here is one which affects all the lines of the metal 
equally. The cathode streamers are conical in shape and taper to a point, the front 
edge of the streamer having an inclination which corresponds to a velocity of 
530 metres per second, and the back edge to 1100 metres per second. The 
positive streamer is weaker than the negative one and has its two edges parallel, 
the inclination of each representing a velocity of 1100 metres per second. The 
effect is very striking in the negative, and it is not easy to explain it in terms 
of under-exposure, or, indeed, in any way which at present would not be purely 
speculative. 



THE STEEAMERS IN THE ELECTRIC SPARK. 83 



NOTES ON THE PHOTOGRAPHS. 

The following notes refer to the spectrum photographs reproduced in Plates 2 to 4. The earlier figures 
in Plate 2 have already been described in the text. 

The capacity and inductance in the discharge circuit, given in the data for each spark, were measured 
with a cymometer, and the period of the oscillations from the negatives themselves in terms of the speed 
of the rotating mirror. The latter was measured before and after each spark by timing the rotations of a 
lower wheel of the gearing, which rotated with the T J<y part of the angular velocity of the mirror itself. 
The periods agree with their calculated values, as a rule, to within one or two per cent. Measurements of 
the durations of the lines are recorded for the " inductionless " spark only, and they represent the times 
from the beginning of the discharge during which a photographic effect is distinguishable on the negative. 
The inductance of the connecting wires in the inductionless spark was also measured with the cymometer. 
It amounted roughly to 25 microhenry. This would make the theoretical period of the oscillations from 
0'3 to 0'46 micro-second according to the capacity in circuit. This is in itself inappreciable, but if there 
were, say, a dozen oscillations the drawing out in the photograph would be easily observed. This is in 
accordance with the photographs which show an appreciable broadening of the base of the metal lines in 
most of the inductionless sparks, but this has not been deducted from the durations. 

The negatives were taken on Wratten's " Verichrome," in some cases on their " panchromatic " plates, 
and the spectrum recorded extends from about A 6300 to A 3500. In the reproductions the top of each 
figure always represents the red end of the spectrum. Only the stronger linen in the spectrum are 
referred to in the lists below. The negatives reveal many of the weaker lines in the spectrum, most of 
which have been identified, but as they do not show in the prints they are not referred to except in 
exceptional cases. The streamers are often composite in character, a strong streamer being formed by the 
overlapping of several weak lines close together. Groups of lines which combine to form a single set of 
streamers are enclosed in brackets. 

The vertical ordinates are the same in all the photographs, but were reduced by the camera in the ratio 
of 0'38. On the other hand, the photographs have been enlarged 1^ diameters in the reproduction, thus 
the figures represent the relative lengths of the sparks, but a spark length 0'57 cm. in the figure 
corresponds to an actual spark length of 1 cm. 

The velocities were determined by careful measurements on the negatives by a reading microscope of 
the inclination of the streamers with respect to the air lines of the spark. They refer to the front edge of 
the metallic vapour in the inductionless spark and to the centre of the streamers in the sparks with self- 
induction. Numbers for the velocities are only recorded when the streamers were sufficiently clear in the 
negatives to enable a fairly definite measurement of several streamers in the same spark to be made (the 
detail of the streamers which permitted the measurements has sometimes disappeared from the repro- 
ductions). The numbers given represent the average velocity over the first two millimetres of the path ; 
the initial velocities are probably two or three times as great, but are very difficult to measure. 

Aluminium. 

Fig. 9. Capacity 0223 microfarad, no inductance, velocity 350 metres per second. 

Fig. 10. Capacity - 0223 microfarad, inductance 95 microhenries, period 8 -95 micro-seconds, velocity 
650 metres per second. 

The only arc line of aluminium, the doublet (3961, 3943), shows plainly as lasting much longer than 
any of the others, its duration in fig. 9 being 100 micro-seconds. In fig. 10 the streamers in it can be 
distinguished, but the whole spark gap is filled with more or less light which lasts in the centre long after 
the actual spark has ceased. The lines of next longest duration (20 micro-seconds) are the group of spark 

M 2 



84 DE. S. R. MILNER ON THE NATURE OF 

lines (3612, 3600, 3584) which forms the strong diffuse streamers at the extreme bottom of the spark. 
The remaining lines visible in the prints are the groups (4622, 4611) at the extreme top of the spectrum, 
with the sharp strong streamers of (4529, 4511, 4478) just below it, an unidentified line of approximate 
wave-length 4200 a little above the arc line, and (3713, 3701) a little below it. These groups possess a 
duration of 12 micro-seconds and they show streamers which are more sharply defined and which die out 
more rapidly than those of the first-mentioned group, but the distinction between spark and condensed 
spark lines appears to be less marked with aluminium than with the other metals. 



Bismuth. 

Fig. 11. Capacity 0-0223 microfarad, no inductance, velocity 220 metres per second. 

Fig. 12. Capacity 0'0223 microfarad, inductance 40 microhenries, period 6'0 micro-seconds, velocity 
GOO metres per second. 

Fig. 13. Capacity 0'0223 microfarad, inductance 95 microhenries, period 9 '14 micro-seconds. 

Fig. 14. Capacity 0'0223 microfarad, inductance 170 microhenries, period 11 '7 micro-seconds. 

The bismuth figures are described in the text, p. 78. The streamer dots apparent in the course of the 
arc line bands 4722, 4120 are not due to the arc lines but to spark lines, (4797, 4750) and 4080, which 
show through them. The equality of the velocities in the streamers corresponding to the various lines is 
plainly shown in the negatives. The streamers in the condensed spark lines are fan-shaped, they are 
quite narrow at the pole and spread out as they recede from it, while those of the other lines have a 
broader base. This is interesting as it shows that the vibrations of the condensed spark lines are only 
induced just at the very centre of the oscillation period when the current and electric force are at their 
maxima. 

Durations in fig. 1 1 : 

Arc lines 105 micro-seconds, spark linos 18 micro-seconds, condensed spark lines 9 micro-seconds. 



Cadmium. 

Fig. l.">. Capacity O'OIOG microfarad, no inductance, velocity 450 metres per second. 

Fig. 16. Capacity 0'0223 microfarad, inductance 95 microhenries, period 8'7 micro-seconds, velocity 
1000 metres per second. 

Fig. 17. Capacity 0'0223 microfarad, inductance 95 microhenries, period 9'2 micro-seconds. 

Fig. 18. Capacity 0'0171 microfarad, inductance 260 microhenries, period 13'2 micro-seconds, velocity 
850 metres per second. 

All the lines of cadmium show the streamers plainly, but there is a great contrast between the sharp 
streamers of the spark lines and the blurred ones due to the lines which persist in the arc. In spite of 
their different character the uniformity of their velocities can be seen in fig. 16. 

The following are the more prominent lines visible : 

Arc lines. Duration 67 micro-seconds. 

5085, 4800, 4678. Partly overlapping blurred streamers. 

(3613, 3610). Strong diffuse streamers at the bottom of the spark. Those of (3467, 3466), 
much fainter, but in the negatives showing an exactly similar appearance to the former, 
can be just distinguished below them. 
Spark lines. Duration 10 micro-seconds. 

(5378, 5337). At the extreme top of the spark. The streamers are very sharply defined and 
visible near the poles only. There appear to be no condensed spark lines. 



THE STREAMERS IN THE ELECTRIC SPARK. 85 

Calcium. 

Fig. 19. Capacity 0-0106 microfarad, no inductance, velocity 780 metres per second. 

Fig. 20. Capacity, 0-0223 microfarad, inductance 260 microhenries, period 15'1 micro-seconds, velocity 
1 700 metres per second. 

Calcium is remarkable for both the great velocity and duration of its streamers. The lines visible in 
the photographs are all prominent arc lines, and they give rise to a general blur which partly masks the 
streamers even at high inductances. The only exception is the double line (3737, 3706), which has a 
much smaller duration than the others. 

The four bands visible in fig. 20 can be identified in the negatives with the following lines or groups of 
lines : 

(1) 5587, 5348, 5269. Duration 170 micro-seconds. 

(2) (4454, 4434, 4425), (4319, 4302, 4289, 4282), 4227. Duration 146 micro-seconds. 

(3) 3968, 3933. Duration 120 miero-seconds. These show the streamers plainly, although the 

spark gap is filled with a general light. 

(4) 3737, 3706. Duration 40 micro-seconds. These lines give quite sharp streamers which are 

overlapped by a general blur due to the strong arc line (3644, 3631, 3623), the difference in 
the behaviour of the two lines being very apparent. 

Lea*/. 

Fig. 21. Capacity 0-0223 microfarad, no inductance, velocity 190 metres per second. 
Fig. 22. Capacity 0'0223 microfarad, inductance 40 microhenries, period (i'3 micro-seconds. 
Fig. 23. Capacity 0'0223 microfarad, inductance 260 microhenries, period 1;VO micro-seconds, velocity 
400 metres per second. 

The following lines are visible : - 

Arc lines. Duration 115 micro-seconds. 
(4062, 4058, 4019). 
3740, (3683, 3671), 3640, 3572. 
These form the two drawn-out bands in which traces of streamers can be seen in fig. 2.'! ; the 

individual lines cannot well be distinguished in the prints. 

Spark lines. Duration 16'5 micro-seconds. Sharp streamers repeated throughout the spark. 
(5608, 5545), 5372. Very faint at the extreme top of the spectrum. 
4386, 4246. The two sets of strong streamers just above the first arc band. 
Condensed spark lines. 

(3854, 3842, 3833). The streamer corresponding to this unresolved group forms an intense 
white dot in fig. 21, a streamer repeated once only in the negative of fig. 22, and it has 
entirely disappeared in fig. 23. The three photographs show how very sensitive the lines 
of this class are to the influence of self-induction. 

Magnesium. 

Fig. 24. Capacity 0-0106 microfarad, no inductance, velocity 450 metres per second. 

Fig. 25. Capacity 0-0223 microfarad, inductance 40 microhenries, period 6'0 micro-seconds, velocity 

800 metres per second. 

r 

Fig. 26. Capacity 0-0223 microfarad, inductance 170 microhenries, period 11 -5 micro-seconds, velocity 
800 metres per second. 

See p. 77. The arc lines in the inductionless spark last 60 micro-seconds, the spark line 4481 only 
15 micro-seconds. The anode discharge is very marked in magnesium, and at the beginning of the 



86 DK. S. R. MILNER ON THE NATURE OF 

discharge is nearly as powerful as that of the cathode. It is worthy of note that, in spite of this, in the 
line 4481 there is a distinct separation between the anode and cathode streamers towards the end of the 
discharge. This shows that the streamer corresponding to this line is only produced when the current 
and electric force exceed a certain minimum value. The same effects are to be seen in the spectra of 
calcium, lead, and mercury. 

Mercury. 

Fig. 27. Capacity 0-0106 microfarad, no inductance, velocity 670 metres per second. 
Fig. 28. Capacity 0-0106 microfarad, inductance 40 microhenries, period 4'1 micro-seconds, velocity 
890 metres per second. 

Fig. 29. Capacity 0-0223 microfarad, inductance 170 microhenries, period 12'2 micro-seconds. 
The sparks were taken from poles of amalgamated zinc, and show the lines of both metals, as follows : 

Arc lines. Duration 58 micro-seconds in fig. 27, diffuse streamers in fig. 28. 
(5790, 5769), 5461, 4359, 4047, 3650 due to mercury. 
4809, 4721 due to zinc, but behaving quite similarly to the mercury as regards duration and 

velocity. 
Spark lines. 

3984 (mercury). The streamers differ very little in sharpness from those of the arc lines in 

fig. 28. In fig. 29 they are sharper and considerably diminished in intensity. 
(4924, 4911) (zinc). Sharp streamers in fig. 28, which disappear with the increased inductance 
in fig. 29. 

Zinc. 

Fig. 30. Capacity 0'0171 microfarad, inductance 40 microhenries, period 4' 8 micro-seconds. 

The arc lines 6363 ;it the top of the figure (very faint), and 4809, 4721, 4609, in the centre in both 
cases form blurred bands overlapping the sharp streamers of the spark lines (6102, 6022) and (4924, 
4911) which show through them. 

Sodium. 

Fig. 31. Capacity 0'0223 microfarad, no inductance, velocity 130 metres per second. 

Fig 32. Capacity 0'0223 microfarad, inductance 95 microhenries, period 9'1 micro-seconds, velocity 
440 metres per second. 

The only line clearly visible is the D line, which has a very great duration (170 micro- seconds in fig, 31). 
In spite of this it shows moderately well-defined streamers in fig. 32. There is a striking difference 
between the air-line spectrum in the two sparks in this photograph, the right-hand one showing a number 
of fine lines which are not air lines, and which are possibly due to the spark having occurred through 
sodium vapour. 

Tin. 

Fig. 33. Capacity 0'0171 microfarad, inductance 40 microhenries, period 5 - micro-seconds, velocity 
800 metres per second. 

The two blurred bands which last in the centre of the spark gap for some time after the oscillations 
have ceased are the two strong arc lines 4525 and 3801. The streamers apparent in the earlier parts of 
their courses are probably due to the spark lines 4586 and 3861, and not to the arc lines themselves. The 
spark lines, like those of bismuth, although not to the same extent, vary considerably in the number of 
repetitions which their streamers undergo. The strongest of the condensed spark lines, which shows very 
brightly and as of very short duration in the inductionless spark, forms the bright but very rapidly fading 
streamers just below the lower arc line (3745 probably). The well-defined streamers at the top of the 
figure are those of the lines 5801, (5589, 5563), 5333. 



THE STREAMERS IN THE ELECTRIC SPARK. 



87 



Antimony. 

Fig. 34. Capacity 0-0223 microfarad, inductance 40 microhenries, period 5-9 micro-seconds, velocity 
1300 metres per second. 

The antimony lines, like those of bismuth, fall into three well-marked classes. The arc lines 4033, 3637 
show as drawn-out bands filling the whole spark gap. 4352, 4265, and unidentified lines with approximate 
wave-lengths 3600, 3400, and 3320, belong to the condensed-spark class, the first streamer being very 
marked and the rest rapidly fading away. The remainder appear to be ordinary spark lines, but are 
difficult to identify. 

Copper, NicM, Platinum, Figs. 35, 36, 37. 

These metals show no well marked lines, and the faint lines are so numerous and close together that they 
are not resolved in the photographs. The oscillations are represented by long lines throughout the 
spectrum, which only show at the top of the spark. The reason of this is probably that the streamers of 
the individual lines are too weak to affect the plate, and that the direction of the drawing out of the spark 
by the mirror is such that at the top of the image the streamers of neighbouring lines fall with their 
lengths over each other, and being thus superposed give a luminosity sufficient to register itself. At the 
bottom of the image the streamers are broadside on and are not superposed. The effect is observable more 
or less in all the photographs. 



Mtlner. 



Phil. Trans., .1, ]'<>!. 2OQ, Plate 2. 




If fill I I \U \ 




!9 



- .,<.,i'ic Co. Imp. 







35 



36 







V. Eutectic Research. No- 1. The Alloys of Lead and Tin. 

Bij WALTER ROSENHAIN, B.A., B.C.E., with P. A. TUCKEK. 

(From the National Physical Laboratory.) 

Communicated by R. T. GLAZEBROOK, M.A., F.R.S. 

Received June 17, Read June 25, 1908. 

[PLATES 5-9.] 

THE investigations described in the present paper were begun in pursuance of a 
scheme for the systematic investigation of the constitution and properties of eutectic 
alloys. The first steps in such an investigation naturally consist in the preparation of 
some samples of typical eutectic bodies in a state approaching purity, followed by the 
determination of their chemical composition and constitution. Since a large number 
of systems of binary alloys have been closely studied and diagrams claiming to set 
forth their equilibrium conditions have been published, it was thought at the outset 
that there would be no difficulty in finding a number of typical eutectic alloys whose 
chemical composition was accurately known and whose constitution could be deduced 
from the corresponding equilibrium diagrams. The eutectic of the lead-tin series was 
chosen as a suitable example for early study partly because the alloys of this series 
are very easily prepared and manipulated, but principally because this series has 
hitherto been regarded as the typical example of the simplest class of binary alloys, 
viz., those in which the two metals are mutually insoluble in the solid state. 

In the preparation of the eutectic alloy of lead and tin on the basis of the data 
given by ROBERTS- AUSTEN* it was found that the results of the present experiments 
did not agree well with the data given by that author. Thus, while ROBERTS- AUSTEN 
gives the composition of the eutectic alloy as approximately 31 per cent, of lead and 
69 per cent, of tin, the present investigation shows the composition of this alloy to be 
very nearly 37 per cent, of lead and 63 per cent, of tin. Further, the diagram given 
by ROBERTS- AUSTEN indicates that solid lead and tin are nearly mutually insoluble in 
the solid state, or, in other words, that the eutectic alloy is present in alloys quite 
near the two ends of the series. As regards the lead end of the series, such serious 

* ROBERTS- AUSTEN, ' Fourth Report to the Alloys Research Committee, Inst. Mech. Eng., 1897.' 
VOL. CCIX A 445, N 17.11.0 



90 



MESSES. WALTER ROSENHAIN AND P. A. TUCKER. 



discrepancies from these views were found when the attempt was made to verify 
them, that it became evident that the investigation of this point had not been pushed 
far enough. It has accordingly been thought desirable to undertake a complete 
redetermination of the equilibria of the lead- tin system with a view to placing our 
knowledge of the constitution of the eutectic on a surer footing. This task was 
rendered more difficult, as well as more interesting, by the discovery of a trans- 
formation which occurs in the alloys rich in lead at temperatures below that of 
complete solidification. 

In the present paper the investigation of the equilibria of the lead-tin system will 
first be described, some observations on the structure and properties of the eutectic 
alloy tft' this series being subsequently given. 

Constitution of the Alloy,* of Lead and Tin. 

Preparation, of lie Alloys. Chemically pure lead and tin were obtained from 
Messrs. Kahlbaum's London agents and on analysis proved to contain only slight 
traces of impurities. The alloys were prepared by weighing out, on an analytical 
balance, the requisite quantities of the two metals and melting them together in a 
suitable manner, the tin being usually melted first and the lead added to the molten 
tin. In all cases the temperature was kept as low as possible, except in some special 
experiments where the effect of exposure to high temperatures was studied with, 
however, only negative results. As a rule the alloys were melted in small fire-clay 
crucibles heated over gas burners, the metal being protected from oxidation by 
various means. In some cases a flux of borax and powdered charcoal was employed, 
while in other cases the metal was melted under oil, glass vessels being employed for 
the latter purpose. In some cases a very small amount of oxidation was found to 
occur in spite of these precautions, but the composition of the alloys has been found 
by analysis not to be materially affected thereby. This is shown in the tabulated 
results of analyses given in Table I. 

TABLE I. Calculated and Analytically Determined Composition of Alloys. 



Calculated. 


Determined. 


Calculated. 


Determined. 


5 per cent. Sn. 


5 - 30 per cent. Sn. 


50 per cent. Sn. 


50-13 per cent. Sn. 


10 






10-29 






55 






55-19 






15 






15-31 






60 






60-02 






20 






20-26 






65 






65-12 






25 






25-15 






70 






70-10 






30 






30-28 






75 






75-23 






35 






35-07 






80 






80-08 






40 






40-10 






85 






85-02 






45 






45-28 






90 






90-11 


4 




63 






63-06 






95 






95-07 


I 








EUTECTIC RESEARCH: THE ALLOYS OF LEAD AND TIN. 91 

It will be seen that the largest difference between calculated and analytically 
determined composition never exceeds 0'3 per cent., and this degree of accuracy is 
adequate for the purposes of these experiments as a whole. Those alloys whose 
composition is required to be more accurately known have been analysed. 

Experimental Methods. The " thermal analysis " of the alloys was carried out by 
means of cooling-curves taken both by the "inverse-rate" and the differential methods. 
Thermocouples of platinum and platinum-iridium were used for the most part, 
although for some special purposes, notably the cooling- and heating-curves at very 
low temperatures, a Constantan-iron couple was used. The indications of the thermo- 
couples were observed by means of the delicate potentiometer installed at the 
Laboratory. The time observations in the case of the inverse-rate curves were made 
with the aid of a chronograph indicating seconds by means of an electrical connexion 
with the standard clock of the Laboratory. The differential curves were obtained by 
observations of the deflection of the differential galvanometer on the same scale us 
that used for the galvanometer connected with the potentiometer already referred to. 
The details of this apparatus and of the method of using it have been published 
previously,* so that no further reference is required here. The thermocouples were all 
carefully calibrated at frequent intervals during the progress of the research, both by 
comparison with the standard couples of the Laboratory and by direct determination 
of well-known fixed points, viz., the boiling-point of water and the freezing-points of 
pure tin and pure lead, the former being taken as 232 C. and the latter as 328 C. 
Graphic interpolation on large-scale curves was used to obtain the values of 
intermediate points on the thermocouple scale. These repeated calibrations gave 
remarkably constant results, and the indications of the platinum couples may therefore 
be regarded as accurate to within 0'8 of a degree, although it must be admitted that 
a slightly greater error may be introduced by the small difference of temperature 
which is liable to exist between a thermocouple and the mass of metal in which it is 
immersed. 

The microscopic examination of alloys containing more than 30 per cent, of tin 
presented no serious difficulty, as it was found possible to polish these alloys by the 
ordinary methods used for the preparation of soft metals. Alloys richer in lead, 
however, proved intractable until special means were employed for polishing them. 
These special means, adopted on the advice of M. F. OSMOND, consisted in the 
preparation of laevigated oxide of chromium in the manner described by 
LE CHATELIER.! When the finer grades of this material are used sparingly on 
" beaver-cloth " discs driven at moderate speeds, it is found possible to prepare 
polished surfaces of the alloys close to the lead end of the series for microscopic 

* CARPENTER and KEELING, "The Range of Solidification and Critical Ranges of Iron-Carbon 
Alloys," 'Journal of the Iron and Steel Institute,' vol. i. ; also STANSFIELD, 'Phil. Mag.,' vol. xlvi., 
pp. 59-82. 

t LE CHATELIER, ' Metallographist,' vol. 4, January, 1901. 

N 2 



92 MESSES. WALTER ROSENHAIN AND P. A. TUCKER. 

examination. When these alloys are polished, the lead, or lead-rich constituent, 
assumes a dark tint, no doubt owing to slight surface oxidation, while any free 
tin present remains bright. When necessary, the contrast thus produced can be 
heightened by etching. These alloys are best etched by the aid of a weak electric 
current passed through a saturated solution of lead nitrate. Nitric acid can also be 
used as an etching agent, but it has the disadvantage that at times it is apt to 
darken the tin as well as the lead. The opening up of the alloys rich in lead to 
microscopic examination, which has thus become possible, has, it is believed, consider- 
ably increased the certainty of the results indicated by the pyrometric study of 
the alloys. 

Experimental Results. 

The Cooling-curves of the Alloys. Five series of cooling-curves were taken, many 
of the individual curves being, however, repeated several times under varying 
conditions. Three of these series are inverse- rate curves, while two are differential. 
The inverse-rate curves of Series A were taken primarily for the determination of the 
" liquidus " curve, i.e., for the determination of the points of initial freezing of the 
alloys ; the observations were, however, carried to temperatures well below that of 
the final solidification of the metal, and on the majority of the curves, therefore, the 
arrest due to the freezing of the eutectic as well as that due to a transformation 
occurring in the solid alloys are shown. In taking these curves uniform quantities of 
200 grammes of each alloy were used and the rates of cooling were kept as constant 
as possible. Typical examples of the curves of this series (A) representing the cooling 
of the alloys containing 10, 20, 30, 50, 63, 75, and 85 per cent, of tin respectively are 
shown in fig. 1. The points of initial freezing derived from these curves are shown by 
the small circles on the line AEB in the equilibrium diagram of fig. 30 (p. 117). The 
curve thus obtained is in good agreement with that given by RoBERTS-AtrSTEN.* 
With regard to the eutectic, it will be seen that in the alloy containing 10 per cent, 
of tin the curve shows a very small eutectic peak, and this peak is much smaller than 
would be anticipated if the eutectic extended to within a fraction of one per cent, of 
the lead end of the series. The curves of this series (A), however, are not regarded 
as giving very reliable data for temperatures below the liquidus for alloys near the 
lead end of the series, and they have accordingly been used only for the determination 
of the liquidus for that range of alloys. In the proved absence of complications at the 
other end of the series, however, the points obtained from these curves have been 
utilised for both liquidus and solidus in the range of alloys containing more than 
65 per cent, of tin. 

Series B and C consist of differential curves, and typical examples of both series are 

* Paper referred to above. 



EUTECTIC RESEARCH: THE ALLOYS OF LEAD AND TIN 




94 " MESSES. WALTER EOSENHAIN AND P. A. TUCKER. 

shown in figs. 2 and 3 respectively in the form of "derived differential" curves.* 
The curves, as reproduced in the figures, are very much reduced from the original 
curves as plotted from the observations ; in order to illustrate the smoothness of the 
curves, as originally obtained, the observed figures of the curves of Series B are given 
in Table II., p. 97, exactly as given in the Laboratory notebook. These figures apply 
to the ordinary, or " direct," differential curves ; the abscissae of the derived curves 
are obtained by subtracting successive readings of the differential galvanometer from 
one another. 

The blank body used in taking these curves was a piece of pure lead of the same 
size as the cylinders of the alloys. In Series B these cylinders were of the size 
generally used in taking the recalescence curves of steel, viz., -| inch long by -f inch 
diameter, the cylinders weighing approximately 35 grammes. In Series C, with the 
object of obtaining greater sensitiveness, the weight of the cylinders was increased to 
175 grammes. In both cases the rate of cooling was very slow, the fall of temperature 
from 180 (J. to 100 C. taking from 30 to 40 minutes. It was at first expected that 
tliis rate of cooling would be sufficiently slow to allow of the attainment of complete 
equilibrium, but subsequent observations showed that this was not quite the case. 

The curves of these two series (B and C) were not taken for alloys containing more 
than 40 per cent, of tin. With higher percentages of tin, the amount of eutectic 
present is so great that the entire cylinder "runs down" when heated above 180 C., 
the metal thus eluding observation by the ordinary differential method during the 
subsequent cooling. Even in the case of alloys containing above 25 per cent, of tin a 
certain amount of the liquid eutectic exudes and runs away from the cylinder, thus 
failing to impart its heat of solidification to the thermocouple on subsequent cooling. 
This fact must be borne in mind in connexion with the approximate quantitative 
interpretation of these curves. 

On examining the curves of Series B it is found that the eutectic peak first appears 

^ The well-known "differential cooling-curves" are obtained by means of the apparatus of EOBERTS- 
AUSTEX, in which a specimen of the alloy under observation is allowed to cool in the same furnace, and, 
therefore, at approximately the same average rate, as a standard neutral or comparison body. Similar 
thermojunctions are inserted in these two cooling bodies and are so connected to the "differential" 
galvanometer as to oppose one another ; any evolution or absorption of heat in the experimental body then 
produces a deflection of the differential galvanometer, as it sets up a difference of temperature between the 
two cooling bodies. In the usual form of "differential cooling-curve" ihe position of the differential 
galvanometer is plotted (or recorded) as abscissa, with the actual temperature of the cooling body- 
indicated by a third thermocouple as ordinate. The "derived differential curves" of the present paper 
simply represent the differential coefficient of the ordinary differential curve, i.e., abscissae represent the 
changes of position of the differential galvanometer which have occurred during successive equal decrements 
of temperature. The nature and use of these curves has been fully described by the author in a paper on 
"Observations on Eecalescence Curves" read before the Physical Society of London, January 24, 1908. 
In accordance with the conclusions of that paper all differential observations in the present paper are 
plotted and interpreted in the form of derived differential curves, while the approximate quantitative 
interpretation of the cooling-curves has also been carried out on the lines laid down in that paper. 



EUTECTIC RESEARCH: THE ALLOYS OF LEAD AND TIN. 



95 




3 

u 



-_ 
*:.' 



IS 
o 



96 



MESSES. WALTER KOSENHAIN AND P. A. TUCKEK. 




S 




o 

i 

*rt 
-f 



T3 
1*4 

O 



1 






-*^> 

I 
B 




I 

i 



o 

c 






EUTECTIC RESEARCH: THE ALLOYS OF LEAD AND TIN. 



TABLE II. Differential Cooling-curve Observations, Series B. 



Absolute 




temperature in 
micro-volts. 


Readings of differential galvanometer. 


Couple M8. 
























Alloy with .... 


8 


10 


12 


15 


17 


18 


19 


20 25 


30 per cent. Sn. 


1275 


15 


12 




- 9 


- 9 


11 


1 


2 -11 


-13 


1250 


13 


11 





- 8 


_ Q 


10 


2 


2-10 -11 


1225 


12 


11 





- 8 


_ o 


9 


21 


2 - 9 


- 9 


1200 


11 


10 





- 7 


- 9 


19 


17 


30 62 


83 


1175 


10 


9 





7 


- 9 


16 


14 


30 


52 


75 


1150 


9 


9 





- 6 


- 9 


13 


11 


24 


48 


66 


1125 


8 


8 





- 6 


- 8 


11 


8 


20 


40 


57 


1100 


7 


7 





- 6 


- 8 


9 


7 


16 


33 


48 


1075 


6 


6 


_ > 


- 5 


7 


8 


8 


13 


27 


41 


1050 


5 


6 





r. 
j 


4 


10 


34 


11 


25 


35 


1025 


4 


5 





- 5 


21 


34 


35 


31 


37 


41 


1000 


4 


5 





- 4 


24 


37 


31 


36 


34 


38 


975 


3 


4 





- 4 


21 


33 


28 


34 


30 


34 


950 - 


2 


4 





- 3 


18 


29 


24 


30 


26 


29 


925 


1 


3 





3 


16 


26 


21 


27 


22 


24 


900 


1 


3 





29 


14 


23 


18 


23 


18 


20 


875 





2 





27 


11 


20 


16 


20 


15 


16 


850 


_ | 


2 





23 


9 


15 


14 


17 


12 


12 


825 


- 1 


1 





19 


7 


14 


11 


15 


9 


9 


800 


- 2 


1 





16 


6 


12 


10 


13 


7 


7 


775 


_ 2 


1 


1 


13 


5 


10 


8 





5 


5 


750 


- 2 


1 


6 


11 














. 


3 


725 


- 3 


1 


17 


9 














700 


- 3 


3 


28 


8 














675 


- 3 


7 


28 


7 














650 


- 4 


17 


20 


5 














625 


o 


15 


16 
















600 


- 3 


10 


13 
















575 


1 


6 


















550 


1 


3 


















525 


6 




















500 


8 




















475 


4 




















450 























425 


- 3 





















in the alloy containing 18 per cent, of tin, while the alloys containing 17, 15, 12, 10 
and 8 per cent, of tin pass through the corresponding temperature without any 
retardation of cooling. The curves of alloys containing less than 8 per cent, of tin are 
not reproduced, as they are entirely blank down to the ordinary temperature. 

In Series C, on the other hand, there is a very small peak at the eutectic 
temperature in the alloy containing 14 per cent, of tin, from which it would seem that 
the greater sensitiveness attained with larger masses of alloy has rendered possible 
the detection of smaller quantities of eutectic. While this is probably the case, the 

VOL. CCIX. A. O 



98 



MESSES. WALTER KOSENHAIN AND P. A. TUCKER, 



microscopic evidence shows that even the most delicate pyrometric methods which 
have been applied in the present research are inadequate to detect the presence of the 
first small proportions of eutectic ; in both series of cylinders (B and C) small traces 
of eutectic could be found in the sections of alloys containing as little as 10 per cent, 
of tin. These small traces of eutectic, however, can be ascribed to the fact that the 
cooling of the alloys had not been slow enough to allow complete equilibrium to be 
established. The effect can be readily explained from a consideration of the process 
of solidification of a solid solution as indicated in the diagram fig. 4. In this diagram 





Fig. 4. 

the line adc represents the liquidus curve of a series of binary alloys of metals 
A and B, while the line abc represents the solidus. The abscissa of the point b is thus 
the limiting solubility of B in solid A, while be is the line of eutectic solidification 
Now, consider the process of solidification of an alloy containing n per cent, of B, 
where n is a little less than b. The cooling of the alloy will be represented on the 
diagram by the line pqn. As the line reaches the point p solidification will begin and 
a solid solution of B in A will be formed having a concentration represented by the 
abscissa of the point r, where a horizontal line through p cuts the solidus curve ab. 
Similarly, as has been indicated by RoofcEBOOM and others, the composition of the 
solid formed at successively lower temperatures will correspond in composition to the 
abscissas of successively lower points on the solidus ab. If sufficient time be allowed, 
the composition of the whole of the solid present at any given temperature will 
become equalised to that which is formed at that temperature ; this equalisation can, 






EUTECTIG RESEARCH: THE ALLOYS OF LEAD AND TIN. 99 

however, only occur by the slow process of solid diffusion, and therefore in most cases 
the solid formed will consist of layers of solid solution whose concentration varies 
more or less continuously, increasing from the centre outwards. If the formation of 
such layers has taken place, and time has not been allowed for diffusion to obliterate 
them, the whole of the alloy will not be solid when the point q is reached, since the 
average composition of the solid formed up to that time will be lower in its content ot 
B than the alloy as a whole ; the remaining liquid portion will therefore contain more 
than n per cent, of B, and as the alloy cools further, fresh layers of solid solution will 
be formed containing more than n per cent, of B. This will continue until the 
remaining liquid attains the concentration represented by b, but as soon as this 
concentration is exceeded, the remaining liquid will solidify as eutectic. This will 
only happen if the rate of cooling is rapid, or if the rate of diffusion is very slow, and 
the concentration (n) of the alloy not far below the saturation point of the solid 
solution. Once, however, that a small proportion of eutectic is formed in this way, 
the meta-stable equilibrium thus established can only be abolished by the process of 
diffusion through successive solid layers, and it is reasonable to suppose that this 
diffusion would be still further retarded by the fact that in the formation of the 
eutectic some of the B constituent has been mechanically separated ; diffusion thus 
has a larger task to perform in overcoming this separation as well as in obliterating 
the concentration gradient existing in the mass of the solid solution itself. 

On the basis of this consideration it is possible to account for the divergence 
between the results of RoBERTS-AuSTEN and those given here. In the experiments 
of ROBERTS- AUSTEN the rate of cooling was probably such as to allow of the formation 
of layers of solid solution differing widely in concentration, with the result that alloys 
lying in reality well within the limits of solid solubility showed the presence of small 
quantities of eutectic. This view is confirmed by the authors' observations on the 
effect of different rates of cooling on the indications of the cooling-curves. With 
moderately rapid cooling the results of ROBERTS- AUSTEN as to the presence of eutectic 
in alloys very near the lead end of the series have been confirmed. With more 
moderate rates of cooling, such as that employed in taking the curves of Series A and 
B, the appearance of the eutectic is postponed to concentrations near 10 per cent, of 
tin, while in the still more slowly cooled series B and C no eutectic becomes apparent 
until much higher concentrations are attained. 

In consequence of these observations it appears necessary, in order to ascertain the 
limit of solubility with accuracy, to expose the alloys to such thermal treatment as 
will facilitate the attainment of complete equilibrium at a temperature just below the 
"solidus." Prolonged exposure to a temperature of 175 C. was chosen for this 
purpose, since this temperature lies safely below the " solidus," even in alloys 
containing eutectic, while it lies well above the temperature of the transformation 
already referred to. The exposure to this temperature was carried out in electrically 
heated ovens whose temperature could be accurately regulated, and in some cases the 

O 2 



100 MESSRS. WALTER ROSENHAIN AND P. A. TUCKER. 

alloys were maintained at 175 C. for a period of six weeks, specimens being removed 
and experimented upon in various ways at intervals. The most important evidence 
derived from these heated specimens is that obtained from a study of their micro- 
structure, but this will be better understood when the complications arising from the 
transformations which occur at lower temperatures in the solid alloys have been 
discussed ; the account of the micro-structure of these specimens will therefore be 
given later. The heat-treated specimens were, however, also used for obtaining 
cooling-curves of these alloys in a state closely approaching complete equilibrium. 
In some cases the cooling-curve was taken without allowing the specimen to undergo 
any intermediate cooling and re-heating, while in other cases specimens were allowed 
either to cool slowly in the ordinary way, or were cooled rapidly (quenched) and 
subsequently re-heated for the observation of the cooling-curve. The initial tempera- 
ture for all these curves was taken slightly above the freezing-point of the eutectic, 
so that the eutectic arrest if any should appear on the curves. The inverse-rate 
curves derived from specimens which had been heated at 175 C. for four and six 
weeks respectively are given in figs. 5, G, and 7. It will be seen that the eutectic 
arrest appears for the first time in these curves in the alloy containing 18 per cent. 
of tin. Microscopic evidence, however, leads to the view that the first appearance 
of eutectic occurs in alloys slightly richer in lead, viz., at a concentration of about 
1G per cent, of tin. 

The cooling-curves of all five series referred to above, in .so far as they relate to the 
alloys rich in lead, show a further recalescence occurring in the solid alloys. In one 
direction this recalescence has been traced down to the alloy containing 8 per cent, 
of tin, while in the other it can just be detected by delicate means in the alloy 
containing 60 per cent, of tin (just below the eiitectic concentration). The tempera- 
ture at which this arrest-point occurs in the cooling of these alloys is lowest in the 
8 per cent, alloy, and attains a maximum temperature at a concentration of about 
18 per cent, of tin, occurring at this highest temperature in all alloys richer in tin up 
to, or nearly up to, the eutectic alloy, where the arrest ceases to be observable. As 
will be seen from the diagram of fig. 30, this maximum temperature is 149 C., while 
the lowest temperature found in the 8 per cent, alloy is 72 C. As the temperature 
at which this recalescence occurs falls to this low point at a tin content of 8 per cent., 
it was at first supposed that the -non-observation of the arrest in alloys of lower tin 
content might be due to the fact that the temperature at which the recalescence 
occurs had fallen down to or even below the ordinary temperature. To decide this 
question, both heating- and cooling-curves of alloys containing 2 per cent, and 4 per 
cent, of tin and also of pure lead were taken down to very low temperatures by means 
of liquid air and a thermo-couple of Iron-Constantan. 

For the purpose of obtaining a cooling-curve over this low range of temperatures 
the specimen of metal into which the thermoj unction had first been inserted was 
wrapped in thick asbestos cloth and first gently warmed to a temperature just above 



EUTECTIC RESEARCH: THE ALLOYS OF LEAD AND TIN. 



101 








102 



MESSRS. WALTER ROSENHAIN AND P. A. TUCKER. 



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EUTECTIC EESEAECH: THE ALLOYS OF LEAD AND TIN. 



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104 MESSRS. WALTER ROSENHAIN AND P. A. TUCKER. 

100 C. By means of a thin wire attached to the specimen, this was then lowered 
into a large Dewar vessel containing a moderate quantity of liquid air ; the specimen 
hung just above the surface of the liquid air, the mouth of the vessel being loosely 
stuffed with cotton-wool in the usual manner. Thus arranged, the specimens, 
weighing about 200 grammes, were found to cool at a convenient rate, and inverse- 
rate observations could readily be taken. Heating- curves were obtained by removing 
the specimen from the Dewar vessel, having first immersed it in the liquid air so as to 
ensure the attainment of the temperature of boiling liquid air ( 189 C.). If the 
specimens were simply allowed to warm in the air of the room the process was found 
to be inconveniently slow, while the heating-curve could not be carried up to the 
ordinary temperature ; the specimens were therefore hung up in a vertical metal 
cylinder placed above a previously warmed crucible ; this arrangement gave a 
convenient rate of heating, and allowed the observations to be carried well above the 
ordinary temperature. One inconvenience arose, however, from the formation of rime 
(ice) on the surfaces of the specimens as soon as they were removed from the liquid- 
air vessel ; when the temperature C. was reached, the melting of this ice caused an 
arrest in the rate of heating which might have masked an arrest due to the alloys 
themselves, but the observation of the corresponding cooling-curve serves to remove 
this doubt. Typical examples of the curves obtained in this way are given in fig. 8, 
and it will be seen at once that they contain no indication of any evolution (or 
absorption) of heat at low temperatures in these alloys. It follows, therefore, that 
the transformation to which these evolutions of heat are due does not occur in alloys 
containing less than 8 per cent, of tin. 

The above conclusion is further borne out by a consideration of the approximate 
quantitative interpretation of the curves already described. TAMMANN* has pointed 
out that the determination of the quantity of heat generated in a recalescence, 
whether it arises from the solidification of a eutectic or from transformations in the 
solid, may yield valuable information as to the constitution of a series of alloys. On 
the other hand, the present author has recently discussedt the theory and interpre- 
tation of cooling- curves, and has shown that any strictly accurate quantitative 
interpretation of the areas of the peaks on inverse-rate or derived differential cooling- 
curves in terms of quantities of heat is not possible, at the same time indicating the 
manner in which rough approximations may be obtained. The results now to be 
quoted must therefore be read with all the limitations which apply to such approxi- 
mations, but even with these limitations they appear to yield some interesting results. 

Apart from errors introduced by variations in the mass of the cooling body and in 
its specific heat, and by variations in the rate of cooling, it has been shown in the 
paper cited above that the areas of the peaks of inverse-rate and of derived differ- 
ential curves represent the quantities of heat generated by the recalescences in 

* ' Zeitschr. Anorg. Chem.,' 37 (1903), p. 303 ; 45 (1905), p. 24 ; 47 (1905), p. 299. 
t Paper cited above. 



EUTECTIC RESEARCH: THE ALLOYS OF LEAD AND TIN. 



105 



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VOL. CCIX. A. 



Fig. 8. " Inverse-rate " cooling-curves. 
P 



106 MESSRS. WALTER ROSENHAIN AND P. A. TUCKER. 

question. A practical difficulty lies in determining the proper boundaries of these 
areas on the side not bounded by the observed curve. In the present instance the 
areas have been closed by lines drawn in free-hand in such a way as to coincide as 
nearly as possible with the limits of the recalescence, these limits being graphically 
estimated on the general lines laid down in the paper cited above. While this is 
obviously only a rough approximation, the errors involved are probably much smaller 
than those which are unavoidably introduced by variations in the rate of cooling as 
from one curve to another of the same series. These variations in the rates of cooling 
have been approximately allowed for in each estimation, but the rates of cooling from 
which this was done are the average rates during that particular experiment, and 
probably differ considerably from the rate at which cooling actually took place during 
the course of the recalescence. The weights of the specimens of metal were accurately 
known in each case, and these have been allowed for in making the estimations of the 
heat equivalents of the recalescence peaks. The actual areas of these peaks were 
obtained by plotting the cooling-observations on a large scale, and measuring the areas 
of the peaks by means of a planimeter. The area so found was divided by the weight 
of the cooling body and multiplied by the inverse of the rate of cooling. The resulting 
approximate values of the quantities of heat evolved have been plotted for the three 
most complete series of curves, and are shown in figs. 9, 10, and 11. Fig. 9 refers to 
the eutectic arrest-points in the derived differential curves of Series A, and for the 
alloys lying between 18 and 25 per cent, of tin the points fall on a straight line, i.e., 
the heat evolved by the solidification of a gramme of eutectic appears to be constant 
for these alloys. The good agreement of this result with theoretical expectations 
serves to show that under favourable conditions the method of approximation yields 
reasonably satisfactory results. If TAMMANN'S method of extrapolation be applied to 
this curve, we find that the zero of the eutectic falls at about 17 per cent, of tin, a 
result which agrees well with other lines of evidence, except that in the present set 
of curves the limit is shifted slightly towards the tin side of the series, because as 
has already been pointed out the rates of cooling used in the experiments were not 
sufficiently slow to allow of the attainment of complete equilibrium. 

When the same process of approximation is applied to the study of the recalescences 
which occur in the solid alloys at a lower temperature, the conditions are not so 
favourable and the results consequently much less concordant. In the alloys contain- 
ing the larger proportions of lead the temperature at which the heat-evolution occurs 
varies considerably from one alloy to another, and this introduces large corrections 
derived from widely differing rates of cooling. It is therefore not surprising to find 
the points in the curves of figs. 10 and 11, which refer to the cooling- curves shown in 
figs. 2 and 6 and 7 respectively, lie somewhat irregularly. In fig. 11 the points 
relating to alloys with 14, 16, and 18 per cent, of tin, which are marked with a small 
circle, refer to cooling-curves taken from specimens which had previously been 
quenched. Their erratic position is probably due to this difference in treatment, and 



KUTECTIC RESEARCH: THE ALLOYS OF LEAD AND TIN. 



107 




they have been ignored in drawing the curve of fig. 11. These curves, however, still 
bear out the conclusion that the evolution of heat reaches a maximum at or near a 
concentration of 18 per cent, of tin, and falls away on either side at such a rate 

P 2 



108 MESSES. WALTER EOSENHAIN AND P. A. TUCKER. 

as to reach a zero value at or about concentrations of 6 and 60 per cent, of tin 
respectively. 

Other peculiarities connected with this evolution of heat are shown by. cooling- 
curves taken under various circumstances. Thus alloys which have undergone 
prolonged heating at 175 C. show this evolution of heat much more markedly, and 
over a shorter range of temperature than alloys which are cooled in the ordinary way 
from the molten state. This indicates that the change which produces this evolution 
of heat is the inversion of a change which is itself gradual, and thus liable to be 
incomplete unless ample time be allowed. This question was tested by taking two 
successive cooling-curves of the same alloy, the first when the alloy had been rapidly 
heated to about 180 C. and allowed to cool at once, the second when the alloy had 
been kept hot for an hour and a half before the cooling was allowed to begin. The 
two curves are shown in fig. 12, and it will be seen that while the recalescence is 
observed in both cases, it is very feeble in the first case and quite well-marked in the 
second. The resulting conclusion that the change on heating is gradual is further 
borne out by the appearance of the heating-curves of these alloys. These are not 
reproduced, since they show nothing well defined ; apparently the change, on heating 
is very gradual and is therefore spread out over a wide range of temperature, merely 
producing slight slopes in the various curves. 

Another fact which appears to be connected with the same properties of the 
substances involved is found in the alloys lying between 8 and 16 per cent, of tin. 
In these alloys the temperature at which the evolution of heat occurs on cooling 
depends upon the time for which they have been exposed to a temperature of 175 C., 
i.e., the alloys which have been kept at that temperature for six weeks show the 
arrest-point at a lower temperature than those which have only been kept hot for 
four weeks, while these in turn show the arrest-points at lower temperatures than 
those which have been simply slowly cooled from the molten state ; still more rapidly- 
cooled alloys show the point at still higher temperatures. The results of a number 
of experiments on this point are plotted in the diagram of fig. 13. The explanation 
for these observations is probably to be found in the formation Of concentric layers 
of solid solutions of different concentrations in more rapidly-cooled alloys. The 
temperature at which the recalescence occurs depends upon the concentration of tin 
in the alloy (in alloys with less than 18 per cent, of tin), and consequently the layers 
richest in tin will undergo the change as soon as the temperature appropriate to their 
concentration is reached and in the absence of homogeneity this will be higher than 
the temperature of reaction corresponding to the average composition of the whole 
of the alloy. It is this beginning of the reaction which is sharply indicated on the 
curves. The shape of these curves, however, strongly suggests that in these cases the 
change which has commenced in the layers of highest tin content is transmitted to 
the other layers, although these had not reached the temperature at which they 
would have spontaneously undergone the change in question. Other observations 



EUTECTIC EESEAKCH: THE ALLOYS OF LEAD AND TIN. 109 



Vi 



K 
* 





110 MESSES. WALTER ROSENHAIN AND P. A. TUCKER. 

tend to confirm the view that the transformation connected with this heat-evolution 
is liable to be suppressed, or at all events to be retarded to a much lower temperature, 
in the absence of an initiating cause. 

The data derived from the cooling-curves as just described appear to admit of a 
variety of interpretations, but their comprehension is so much assisted by the 
microscopic data that it will be preferable to deal with their interpretation in that 
connection. 

The Micro- Structure of the Alloys. 

The general micro-structure of the alloys is represented in figs. 14 to 22 inclusive 
(Plates 5-6*). The alloys near the lead end of the series will be discussed below. 
Fig. 14 shows the structure of the alloy with 15 per cent, of tin when rendered 
approximately homogeneous by four weeks' exposure to 175 C. (magnification x 100 
vertical illumination). The dark ground-mass represents the solid solution of tin in 
lead ; the bright dots correspond to the residue of free tin remaining unabsorbed 
from the eutectic which was formed during the initial relatively rapid solidification 
of the alloy. On more prolonged heating to 175 C., followed by rapid cooling, this 
alloy becomes entirely homogeneous. The next figure (No. 15) shows the alloy with 
20 per cent, of tin, in which no amount of prolonged heating appears to be capable 
of entirely removing the free or eutectic tin. This photo-micrograph has been taken 
under a higher magnification in order to show the remains of the eutectic structure in 
the light areas which represent the free tin. Owing to the prolonged heating which 
this specimen has undergone, the lead constituent of the eutectic has almost entirely 
coalesced with the ground-mass, leaving the residual free tin in segregated masses 
containing only a few small globules of lead. The appearance of these segregated 
masses of eutectic tin is very characteristic, and can be readily used for the identifica- 
tion of free tin which is derived from eutectic as compared with free tin subsequently 
separated from the solid solution ; apart from the difference in size of the masses, the 
secondary tin separated from the solid solution never shows the black dots and 
patches found in the primary or eutectic tin. 

Fig. 16 shows the alloy with 45 per cent, of tin (magnification 200 diameters). 
This example is given as typical of the structure of the alloys lying between the 
eutectic alloy and a tin content of 20 per cent. In all these alloys the primary 
crystals of lead appear as dendritic crystallites of the type shown in this figure, 
appearing embedded in typically laminated eutectic. A special feature of these alloys 
is the fact that the lead crystallites are surrounded by zones ot pure tin, i.e., of 
eutectic whose lead constituent has coalesced with the lead of the crystallite. This 
feature is of considerable importance, because it explains the manner in which the 
sheaths of pure tin isolate the free lead of the crystallites from the lead constituent 

of the eutectic. 

* See Description of Plates, p. 122. 



EUTECTIC RESEARCH: THE ALLOYS OF LEAD AND TIN. 1U 

Fig. 17 shows one of the typical forms of the eutectic alloy (magnification 300 
diameters) containing 62 '97 per cent, of tin. The various forms taken by. this alloy 
will be discussed in detail in the special section at the end of this paper. 

Fig. 18 represents the alloy containing 65 per cent, of tin. As the micro-structure 
shows, this alloy is just above the eutectic composition, white crystallites of free tin 
appearing embedded in the eutectic. (Magnification 200 diameters.) 

Fig. 19 represents the alloy containing 74 per cent, of tin, under a magnification 
of 200 diameters. The crystallites of free tin are seen in larger quantity and are 
surrounded, or nearly surrounded, by regions of the lead constituent. 

Fig. 20 shows the alloy containing 85 per cent, of tin. Here the white crystals 
of tin occupy the greater part of the area of the section, the eutectic merely forming 
a meshwork l>etween the crystals. In the 95 per cent, alloy shown in the next figure 
(No. 21, magnification 200 diameters) the meshwork of eutectic, or, rather, of the 
lead constituent of the eutectic, is very thin and no longer continuous. Finally, in 
fig. 22, the alloy containing only 1 per cent, of lead (99 per cent, of tin) is shown. 
The eutectic can be definitely traced in this micrograph, and the structure of this 
alloy is not affected in this respect by prolonged heating at 175 C. This fact, 
together with the cooling-curves already described, leads to the conclusion that the 
eutectic extends very nearly to the tin end of the series, and that the solubility of 
lead in tin is zero or very nearly zero. 

For the purpose of determining the limiting solubility of tin in lead, the alloys in 
the neighbourhood of a tin content of 15 per cent, were carefully examined after six 
weeks' exposure to heat at a temperature of 175 C. Examined under moderate 
magnifications, by whose aid the presence of "primary" tin could not fail to be 
recognised, the 15 per cent, alloy was found to be entirely homogeneous, the few 
white spots seen after four weeks' heating (as seen in fig. 14) having entirely 
disappeared. In the 1 6 per cent, alloy small specks of primary tin could generally be 
observed, the appearance of this alloy after six weeks' heating being similar to that 
shown in fig. 14. By powdering this alloy, compressing the powder so as to form a 
solid, and then further heating at 175 C., the 16 per cent, alloy can, however, be 
rendered quite homogeneous under moderate magnifications. In alloys with 17 and 
18 per cent, of tin the specks of primary tin are always clearly present, and in 
increasing quantity with increasing tin content. The conclusion drawn from these 
observations, taken together with the data derived from the cooling-curves described 
above, is that the limiting solubility of tin in lead at a temperature of about 180 C. 
(which is near the temperature of the freezing of the eutectic, and therefore very close 
to the solidus in alloys containing nearly 16 per cent, of tin) is very little more than 
16 per cent. On this view an alloy containing a little less than 16 per cent, of tin, 
if cooled so slowly that complete equilibrium is attained, would solidify as a 
homogeneous mass, no eutectic being separated. It will be seen, however, that there 
is good reason to suppose that some "secondary" tin is separated from this solid 



112 MESSRS. WALTER ROSENHAIN AND P. A. TUCKER. 

solution at lower temperatures if the alloy is slowly cooled, and this fact has 
considerably complicated the determination of the limiting solubility. The fact that 
very gradual cooling would be required to produce this complete equilibrium is borne 
out by microscopic evidence, as well as by the cooling-curves described above. 
Figs. 23 and 24 (Plate 6) are photo -micrographs, at a magnification of 150 diameters, 
of alloys containing 10 and 15 per cent, of tin respectively, cooled from fusion in 
an ordinary laboratory furnace. Considerable quantities of eutectic appear in both, 
but, as has already been indicated, these alloys gradually become homogeneous on 
exposure to a temperature of 175 C. 

In the alloys lying Ixjtween 8 and approximately GO per cent, of tin the cooling- 
curves show the existence of changes involving an evolution of heat at a temperature 
which lies at 149 C. for alloys above 18 per cent, of tin, and at lower temperatures 
for alloys of lower tin content. In order to correlate these evolutions of heat with 
changes in the micro-structure of the alloys it was necessary to cool specimens of the 
alloys from a temperature just above the recalescence point at so rapid a rate as to 
more or less suppress the change in question. It was evident that from a temperature 
so low as 149 C. mere quenching in cold water would not be sufficient for this 
purpose, and quenching in liquid air was therefore employed. 

For this purpose a Dewar vessel containing a considerable quantity of liquid air 
was brought to the door of a small electric oven in which the specimens had been 
heated ; the quenching operation was carried out by removing from the oven a small 
slab of uralite on which the specimens had been placed for this purpose and allowing 
the specimens to slide quickly and directly into the liquid air. The specimens were 
made of small dimensions, and the violent ebullition of the liquid air which they at 
first produced subsided very rapidly. As soon as the specimens had become quiescent 
in the bath they were removed from the liquid air and allowed to lie on the table 
until they had regained the ordinary temperature, when they were prepared for 
microscopic examination, as previously described. The object of using liquid air in 
this instance, it should be noted, was simply to ensure the most rapid possible rate 
of cooling, and not in any way to test the effect of liquid-air temperatures upon the 
alloys. It was, however, necessary to ascertain whether the mere fact of exposure to 
such a low temperature produced any change in the micro-structure of the alloys, and 
to test this point duplicate specimens of the alloys were immersed in liquid air for a 
similar length of time, but the immersion in this case only took place after the 
temperature of transformation had been passed ; specimens of pure lead and of pure 
tin were included in this experiment. A third set of similar specimens was then 
allowed to cool very slowly in the electric oven itself, and the micro-structure of the 
three sets was subsequently compared. In the case of pure tin, the experiment was 
tried in view of the fact that tin is known to exist at low temperatures in the allo- 
tropic form of a grey powder, and it was supposed that some sign of this phase might 
be detected in the specimen cooled in liquid air ; this was not the case, however, and 



EUTECTIC RESEARCH: THE ALLOYS OF LEAD AND TIN. 113 

the conclusion is justified that the duration of the exposure to liquid air was not long 
enough to allow this transformation to occur. 

The comparison of the micro-structure of the specimens quenched from a tempe- 
rature just below the recalescence in question with that of very slowly- cooled 
specimens also shows only very slight differences, so that the conclusion is justified 
that the differences observed between the structure of specimens quenched above the 
recalescence temperature and those which have been allowed to undergo the change 
unhindered are due entirely to the partial suppression of the transformation associated 
with these evolutions of heat. 

The alloys chosen for close study in this respect were those containing 16 to 18 per 
cent, of tin, since in this range the heat-evolution reaches its maximum intensity. A 
high degree of magnification is required to bring out clearly the difference in micro- 
structure between the alloys which have been quenched above the transformation 
point and those which have been allowed to undergo the change. (See Plate 7.) 

Fig. 25 is a photo-micrograph (magnification 1000 diameters) of a specimen of an 
alloy containing 16 per cent, of tin which has been kept at 175 0. for six weeks, and 
has then been quenched in liquid air from a temperature of 160 C. Seen under a 
low magnification this specimen appears practically homogeneous, but the high power 
used in the photograph reveals the presence of a large number of very fine white 
patches; from their behaviour and appearance these undoubtedly consist of free tin, 
but their minute size and their distribution over the specimen, as well as the entire 
absence of any spots or markings within the white patches, indicate that this tin is of 
" secondary" origin, having been separated from the solid solution during cooling. To 
some extent the presence of this tin in the quenched specimen is probably to be 
ascribed to the fact that the rate of cooling employed was not great enough to 
entirely suppress the change occurring at the recalescence. Figs. 26 and 27 are 
photo-micrographs of a piece of the same ingot as that represented in the previous 
figure, but in this case the specimen has not been quenched, but has undergone very 
gradual cooling from 150 C. to the ordinary temperature. The mottling of secondary 
tin is much more pronounced in these specimens, the quantity of tin being much 
larger, while it is also aggregated into larger masses. Since the appearance of a 
specimen quenched from a temperature just below the recalescence is very similar* to 
that of this specimen, it follows that the transformation in question has involved the 
rejection of a considerable quantity of tin from the solid solution. 

Figs. 28 and 29 respectively represent typical sections, under a magnification of 
1000 diameters, of quenched and slowly-cooled alloys containing 18 per cent, of tin. 
In the quenched specimen (fig. 28) we have two large masses of primary tin (remnants 
of eutectic) surrounded by the ground-mass of dark solid solution mottled with minute 
patches of secondary tin ; in the slowly-cooled specimen (fig. 29) the quantity of 

* The laminae of secondary tin, seen in fig. 27, are, however, only found in very slowly-cooled, 
specimens they evidently result from aggregation during this process. 
VOL. CCIX. A, O 



114 MESSES. WALTER ROSENHAIN AND P. A. TUCKER. 

secondary tin is much larger, while it has segregated into masses which compare in 
size with the primary tin in the same section ; it would seem, in fact, that in this 
case a considerable proportion of the secondary tin had formed around the primary 
tin present, or had coalesced with it. In this alloy, as in the 16 per cent, alloy, it 
thus appears that the transformation which takes place at 149 C. involves the 
rejection of tin from the solid solution. 

In view of these facts, and of the data supplied by the cooling-curves, the nature of 
the transformation in question may be considered. Three alternative explanations 
suggest themselves, viz. : 

(a) That the recalescence is due to the formation on cooling of a compound 

which only gradually dissociates on heating ; 
(6) That the recalescence arises from the decomposition of a compound which exists 

at higher temperatures, but which is only slowly formed on heating ; and 
(c) That the transformation is a change in the solid solution from a /8 to an a 

modification, the latter possessing a smaller solubility for tin than the 

former. 

Hypothesis () may be rejected at once on the grounds that the maximum heat 
effect of the transformation does not occur at a concentration of tin which corresponds . 
to any simple atomic formula, while the formation of a compound at the critical point 
in these alloys would lead us to anticipate that the slowly-cooled alloys in which 
the reaction had been permitted to take place would be more homogeneous than 
the quenched alloys in which the reaction had been inhibited, whereas the reverse is 
the case. 

Hypothesis (b) would agree with the microscopic evidence, but the difficulty still 
remains that the maximum does not coincide with any simple atomic ratio. The 
nearest simple formula would be Pb 3 Sn, and this would place the maximum at a 
concentration close to 1G per cent, of tin. This hypothesis has, however, to face the 
difficulty that there is no change of shape in the liquidus curve to correspond to the 
existence of such a compound ; the liquidus, as determined in the present experiments 
and in those of ROBERTS- AUSTEN already cited, shows no signs of either a maximum 
or a break of continuity, while there is also no sign of any absorption of heat at any 
temperature between the liquidus and the solidus which might account for the 
formation of such a compound in that range of temperature. On this ground, 
hypothesis (fc) must also be rejected. 

The remaining explanation is the one which appears best to fit the facts. On this 
view the solid solution of tin in lead, when it contains more than 8 per cent, of tin, is 
capable of existing in two forms which may be called a and ft respectively. The 
saturated (/8) form of this solution, containing 16 per cent, of tin (approximately), 
passes into the a form on cooling to 149 C., and at that point rejects a certain 
amount of the dissolved tin in a finely divided " secondary " state. It is probable 



EUTECTIC EESEAECH: THE ALLOYS OF LEAD AND TIN. 115 

that the solubility of tin in the a body decreases still further as the temperature falls, 
but this decrease is certainly slight its possible existence, however, makes it difficult 
to give any estimate of the solubility of tin in the a body at its transition temperature. 
On heating, the reverse change (from a to /3) only takes place gradually, a fact which 
is partly accounted for by the slowness with which the ft Ixxly takes up its full amount 
of tin. When the concentration of tin in the ft body is lower than 16 per cent., the 
transformation on cooling is retarded until a lower temperature is reached ; at the 
same time the intensity of the reaction falls off until, with a tin content less than 
8 per cent., the ft form appears to remain stable down to the temperature of liquid 
air. The fact that the intensity of the reaction falls oft' so markedly as the concen- 
tration of tin falls below IG per cent, suggests that the actual separation of the tin 
itself is to some extent the source of the heat evolved, but it is not at present possible 
to discriminate between the various possible sources of heat in a complex reaction. 
The fact, however, that botli the temperature and intensity of a change of this kind 
varies with the concentration of the dissolved element finds it analogue in the higher 
arrest-points of low-carbon steel. 

A point of some difficulty yet remains to be dealt with. The data of the cooling- 
curves show that this heat-evolution diminishes to zero at or near the concentration 
of the eutectic alloy, and it is therefore evident that the transformation is confined to 
the structurally free lead constituent, the lead-rich constituent of the eutectic taking 
no part in the reaction. This fact can only be reconciled with the Phase llule by 
supposing that while the structurally free ft solution and the lead- rich constituent of 
the eutectic must be the same phase when first formed, yet the lead constituent of 
the eutectic retains the /3 state (in meta-stable equilibrium) when the transition 
temperature is passed. This explanation is rendered probable by the observation 
already described, that the crystallites of the lead constituent are generally completely 
surrounded by a sheath of pure tin which separates them from the lead constituent of 
the eutectic ; this envelope of tin no doubt serves to prevent the propagation of the 
reaction from the structurally free ft body to the corresponding constituent of the 
eutectic. 

The view that owing to the retention of the ft state in a meta-stable form the lead- 
rich constituent of the eutectic is not identical with the stable a body is further borne 
out by an examination of the densities of the alloys, which have been carefully 
determined for this purpose. The density of the a body containing 16 per cent, of 
tin (part of which is present as free "secondary" tin) is found to be 10 '31, while the 
density of pure tin is 7 '30. Taking the percentage composition of the pure eutectic 
at 37 '07 per cent, of lead and 62'93 per cent, of tin, and supposing the lead-rich 
constituent of the eutectic to hold 16 per cent, of tin in solution, the percentage 
composition of the eutectic in terms of its actual constituent phases becomes 44 - 13 per 
cent, of lead-rich ft constituent and 55 '87 per cent, of tin. From the observed density 
of the eutectic, an obvious calculation shows that the density of the lead-rich 

Q 2 



116 MESSES. WALTER EOSENHAIN AND P. A. TUCKER 

constituent must be 10 '38. The density of the lead-rich constituent of the eutectic, 
i.e., of the ft body in the meta-stable state, is thus 0'07 higher than that of the stable 
a body with the same amount of tin. This result fully agrees with the view that the 
a body has deposited some of its tin content in the free state, with an increase of 
volume. 

The equilibrium diagram of the lead-tin alloys, as based upon the data and inferences 
given above, is shown in fig. 30. The diagram consists in all of eight fields or regions 
corresponding to different states of the alloys. In field No. 1, lying above the 
liquidus AEB, the alloys are homogeneous liquids. In field No. 2, bounded by the 
lines AE, EC, CA, the alloys consist of a mixture of liquid and crystals of the lead- 
rich ft body ; it should, however, be noted that while the line EC and the position of 
the point C have been determined, the line AC has not been fixed experimentally and 
is therefore drawn as a dotted line, but its true position is not likely to depart widely 
from that indicated. In field No. 3, bounded by AC, CF, FE, EPb, PbA, the alloys 
consist of the homogeneous ft body, which is a solid solution of tin in lead which is 
saturated at a temperature of 182 "5 C. with a tin content of a little more than 
1G per cent. The point F, lying upon the line of the a./ ft transformation at the point 
where that transformation first readies its highest temperature (at a concentration of 
18 per cent, of tin), probably represents the limit of saturation of the ft body at 149 C., 
and for that reason the limit of the region of pure ft has been drawn from C to F ; 
this line also is to be regarded as tentatively drawn. The curve from F towards E 
has been prolonged vertically downward, since no trace of the ft/a reaction can be 
found in alloys containing less than 8 per cent, of tin. 

In region No. 4, bounded by CE, EG, GF, FC, the alloys consist of saturated ft 
plus eutectic or in terms of phases of saturated ft and tin. In region No. 5, 
bounded by FG, GK, KE, EF, the alloys consist of the a body (a saturated solution 
of tin in lead saturated at a lower concentration of tin than 18 per cent.) plus eutectic 
plus secondary tin, the eutectic itself consisting of tin plus the body in a meta-stable 
condition. In terms of phases this region would contain the a body plus tin if 
complete equilibrium were attained, but in all cases so far studied meta-stable ft was 
present. Region No. 6, bounded by BE, ED, DB, contains alloys consisting of liquid 
plus crystals of pure or very nearly pure tin. Region No. 7, bounded by ED, DH, HG, 
GE, comprises alloys consisting of tin plus eutectic or in terms of phases of tin plus 
the ft body in a stable state. Finally, in region No. 8, bounded by GH, HSn, SnK, 
KG, the alloys contain tin plus eutectic or in terms of phases tin plus meta-stable 
ft body. 

The Eutectic Alloy of Lead and Tin. 

The percentage composition of the eutectic alloy has been determined with special 
care. The method adopted consisted in preparing an alloy of a composition known to 
be approximately that of the eutectic and preparing a micro-section. On examining 



EUTECTIC RESEARCH: THE ALLOYS OF LEAD AND TIN. 



117 



the section it was possible to detect the presence of a very slight excess of either of 
the constituents, thus differentiating between alloys which could not be definitely 
separated by the indications of the pyrometer alone. It was found that in a small 



300- 



JOO'- 



/ftf- 



/Of- 



*t 

n't 



(f) 



(.1) fi+LifuiJ 



(3) ft 



\ff 



(61 fin + Lia uLal 



\ M/3+uiectic (fi + 



(f) Of + Euieetic 



(1} 



H 



S + Euttdic 



K 



(0 

ro 



io 

V 



3o 



1*0 

io 



fo 

f.o 



io 

+0 



70 

3? 



SO 

10 



10 
/o 



/oo 
o 



Fig. 30. 

ingot of such an alloy, particularly if slowly cooled from fusion, there was generally a 
slight concentration of tin towards the top of the ingot and a corresponding small 
concentration of lead near the bottom. By the aid of the microscope, however, 
specimens free from excess of either constituent could be picked out, and these were 
submitted to careful chemical analysis. The composition as thus determined is found 

to be : 

Lead 37'07 per cent. 

Tin 62-93 

and this result agrees closely with the figures given by GUTHBIE, and derivable from 
ROBERTS- AUSTEN'S diagram, although it is believed that owing to the greater refine- 
ment introduced by the use of the microscope the present determination is probably 



1 1 8 MESSRS. WALTER ROSENHAIN AND P. A. TUCKER. 

more accurate, since even very delicate pyrometric observations fail to detect any 
difference in freezing-point between alloys lying between 62'5 and 63'5 per cent, of 
tin ; GUTHRIE'S method of separation, by liquation, was necessarily subject to the 
same inaccuracies. 

From the data as to the chemical composition, constitution and density of the 
eutectic alloy and its two component phases as arrived at in the earlier parts of this 
paper, it is possible to calculate the volume composition of the eutectic alloy. The 
eutectic has been found to consist of 55'87 parts of tin and 44'13 parts of /8 per cent., 
the densities of tin and of the fl body being 7'30 and 10'38 respectively, while the 
density of the eutectic is 8'40. The volumes of free tin and of the /3 body present in 
LOO grammes of the eutectic alloy are therefore equal to 55'87/7'30 and 44'13/10'38 
respectively ; this gives the volume ratio of the two constituents as 7 '653 to 4'252 or 
1. '80 to 1. An attempt was made to verify this volume relationship by means of 
pliinimetric measurements of the relative areas of the light and dark constituents 
of the eutectic as represented in some of the best defined of the photo-micrographs 
reproduced in figs. 34, 35 and 30, but the results varied too widely to allow of any 
satisfactory deduction. Consideration of the fact that the structure of the eutectic as 
shown in these photographs frequently assumes the form of plates or rods of one 
constituent embedded in the other at once serves to explain these variations ; in the 
case of a bunch of parallel needles of the /3 body lying in a matrix of tin, the relative 
areas of the cross-sections as seen in a micrograph would depend upon whether the 
plane of the section ran parallel to or at right angles to the length of the needles. 
These variations are, of course, further accentuated by the fact that the eutectic 
structure is always somewhat minute, so that the areas measured at any one time are 
confined to a very minute portion of the actual alloy. 

Examples of the typical micro-structure of the lead-tin eutectic alloy are given in 
figs. 31 to 36 inclusive (Plate 8), all of which have been taken from samples of 
pure eutectic prepared in the manner described above. Fig. 31 (magnification 600 
diameters) shows an example of regular lamination, the layers of the two constituents 
lying approximately parallel ; the photograph, however, shows the junction of two 
regions or "grains" in the eutectic, the general direction of these parallel bands being 
decidedly different in the adjacent " grains," while more or less constant throughout 
each region or " grain." In figs. 32 and 33 (magnification 300 diameters) a similar 
feature is shown over a larger area, fig. 33 showing the junction of three areas of 
different and more or less regular orientation. In figs. 31 and 32 it should be noticed 
that the regular pattern of the eutectic remains undisturbed up to the very edges 
of each region (the black dots in fig. 3 1 are small holes in the metal, not areas of /3). 
As close observation has shown, this is a severe test of the accuracy with which the 
true eutectic composition has been attained in the synthesis of the alloy, the first 
effect of a slight addition of either constituent being to produce a slight coarsening 
of the structure combined with a slight relative increase in the amount of the excess 






EUTECTIC EESEAECH: THE ALLOYS OF LEAD AND TIN. 119 

constituent at the boundaries of these regions of similar orientation. To a very 
small extent this is the case in fig. 33, but it is clearly illustrated in figs. 36 and 37, 
which represent alloys containing a slight excess of tin (No. 36 represents an alloy 
with 64 per cent, of tin, magnified 200 times, while No. 38 represents an alloy with 
65 per cent, of tin, magnified 600 times). 

Figs. 34 and 35 show, under higher magnification (600 and 1200 diameters 
respectively), other types of eutectic structure of the " laminated " variety, but iu 
this case the lamination is not rectilinear, while still preserving a certain regularity 
throughout well-defined regions. Study of these structures suggests certain con- 
clusions as to the manner in which they have originated and as to their physical 
nature. Important evidence as to this may be obtained by viewing a specimen of 
pure eutectic, properly polished and etched, under oblique illumination with a low 
magnification. Fig. 39 is a photo-micrograph of such a specimen taken with a 
magnification of 12 diameters. A single photograph, however, gives a very feeble 
idea of the true appearance of such a specimen. Viewed in this manner the various 
regions of similar orientation already referred to are clearly differentiated in colour 
and brightness, owing apparently to the manner in which the incident light is 
reflected by the facets arising from the etching out of one constituent. The lustrous 
appearance, with its brilliant diffraction colours, however, is strikingly different from 
the "oriented lustre" observed when a similar section of pure metal is viewed in this 
way. The conclusion which is to be drawn from this difference is probably that while 
the eutectic has some form of crystalline structure, that form is different from that of 
pure metals. When the specimen of eutectic is rotated under oblique light, this 
difference becomes still more evident, and its character is revealed. In pure metals 
the various regions or grains which are now well understood to lie simply holo- 
morphic crystals characteristically exhibit a uniform brightness over their entire 
area, and, when the specimen is rotated, increase and decrease in brilliance according 
to the incidence of the light uniformly so far as the entire area of eacli crystal is 
concerned. The regions or grains of the lead-tin eutectic behave differently ; in every 
position of the specimen the incident light appears to pick out some radial line or 
sector in each grain, and this line or sector appears bright ; as the specimen is rotated 
the lighted sector appears to rotate in each crystal, thus giving rise to an appearance 
strikingly similar to that which is observed when a transparent section of a spherulitic 
mineral crystal is rotated under crossed Nicol prisms, except that the dark cross is 
not seen as such in the eutectic " grains." Examination of a number of such 
specimens has led the author to the view that the grains or regions into which 
masses of pure eutectic are always found to be divided probably represent true 
spherulitic crystals, i.e., crystals which possess a radiating structure, but which in 
other respects are similar to the holomorphic crystals of pure metals. The effect of 
the radial structure on the mechanical behaviour of the metal must, however, be very 
marked. The detailed study of the phenomena accompanying plastic deformation 



120 MESSRS. WALTER ROSENHAIN AND P. A. TUCKER. 

of these alloys is, however, rendered very difficult by the presence of the second 
constituent. In the present case the ft body is so much softer than the tin that on 
deformation it is immediately driven out at the surface, thus obscuring the deforma- 
tion phenomena of the tin matrix which constitutes the greater bulk of the alloy. 

A study of the micro-structure of the lead-tin eutectic shows as would be 
anticipated from the volume-relation of the two substances that in most sections the 
yS body can be seen definitely embedded in and surrounded by the tin, which has 
therefore been called the matrix. Whether the two bodies actually crystallise 
simultaneously or whether there is a slight interval of time or of temperature 
between their solidification has yet to be ascertained, but it would appear probable 
that at each point of the eutectic where solidification was beginning the crystallisa- 
tion of the predominant constituent determined the arrangement of the whole mass ; 
on that view, in the present case, the tin crystallised out in the form of radiating 
dendrites whose arms met and more or less interpenetrated those of adjacent 
dendrites, the lead liquid or solid being forced into the interstices, whose shape 
would vary according to the form of each particular dendrite. Whether this picture 
of the solidification process be accurate or not, the existence of clearly marked 
spherulitic structure throughout the individual grains of the eutectic proves quite 
definitely that the solidification of each grain must have proceeded from a centre, and 
that therefore one or both of the constituents are arranged in some definite crystalline 
manner throughout each grain ; the alternative view that each separate particle 
of eacli constituent might be a minute independent crystal, having 110 systematic 
connection with its neighbours, being thus entirely discredited. 

In the hope of throwing further light on the nature and structure of eutectic alloys, 
the micro-structure of lead-tin alloys of eutectic composition was investigated under 
other conditions. In one experiment the specimen of alloy, which originally showed 
the laminated structure usually associated with the term " eutectic," was exposed to 
prolonged heating at a temperature of ] 75 C. (just below the melting-point of the 
eutectic). On subsequent examination it was found that the /8 body of the alloy had 
segregated into relatively large masses in the manner shown in fig. 38. In all other 
respects the alloy had preserved its true eutectic character, thus serving to show that 
the ordinary "typical" eutectic structure is a consequence only of the manner in 
which these alloys usually solidify from fusion, and is not an inherent property of 
alloys of that particular composition. 

In connection with this line of enquiry it occurred to the author that a solid alloy 
of lead and tin of the eutectic composition might be produced by the method of 
SPRING,* i.e., by strongly compressing clean fresh filings of the two metals by means 
of an hydraulic press. A small compressing apparatus was therefore prepared (by the 
kind co-operation of Dr. T. E, STANTON), and powdered lead and tin, mixed in the 
correct proportion of the eutectic composition, were compressed in it by the aid of a 

* SPRING, 'Bull, de 1'Acad. Roy. de Belgique,' (2), vol. xlv. (1878), No. 6. 



EUTECTIC RESEARCH: THE ALLOYS OF LEAD AND TIN. 121 

small testing-machine, pressures up to 35 tons per square inch being put on the metal. 
The small buttons of solid metal produced in this way were subsequently cut and 
polished for microscopic examination, and their appearance under a magnification of 
80 diameters is shown in figs. 40 and 41. Fig. 40 is taken from a part of the 
specimen which had been subjected to severe flow under the action of the plunger, 
while No. 41 is taken from a part where the pressure had acted uniformly in all 
directions. It will be seen at once that this compound mass of metal can scarcely be 
regarded as a true alloy at all ; the .particles of lead and tin are merely juxtaposed 
and held together by surface cohesion. It is intended to observe these specimens 
from time to time, both when kept at the ordinary temperature and when maintained 
at temperatures just below the melting-point of the eutectic, with a view to detecting 
the process of diffusion which will probably occur, but so far the time has been too 
short to allow of definite results being observed. 

For the purpose of furnishing a more delicate test of such a diffusion process, 
specimens of an alloy containing 1 7 per cent, of tin were prepared in a similar 
manner ; their micro-structure is shown under a magnification of 80 diameters in 
fig. 42. Prepared from fusion and very slowly cooledj this alloy would be very nearly 
homogeneous, so that the difference between the true alloy and the mechanical 
mixture obtained by the compression process is very marked in this case. 

The author is indebted to Dr. E. T. GLAZEBROOK, F.E.S., the Director of the 
Laboratory, for his kindly interest in the progress of the present research, and to his 
colleagues on the staff of the Laboratory for much valuable help in various details 
of the work. 



VOL. CCIX. A. II 



122 ETJTECTIC RESEARCH : THE ALLOYS OF LEAD AND TIN. 

DESCRIPTION OF PLATES (5-9). 
PLATE 5. 

Fig. 14. Alloy with 15 per cent. Sn after four weeks at 175 C. V. x 100 diameters. 

15. Alloy with 20 per cent. Sn after prolonged heating. V. x 300 diameters. 

16. Alloy with 45 per cent. Sn. V. x 200 diameters. 

17. Alloy with 63 per cent. Sn (eutectic alloy). V. x 300 diameters. 
18. Alloy with 65 per cent. Sn. V. x 200 diameters. 
19. Alloy with 74 per cent. Sn. V. x 200 diameters. 

PLATE 6. 

Fig. 20. Alloy with 85 per cent. Sn. V. x 200 diameters. 

21. Alloy with 95 per cent. Sri. V. x 200 diameters. 

22. Alloy with 99 per cent. Sn. V. x 200 diameters. 

23. Alloy with 10 per cent. Sn cooled from fusion. V. x 150 diameters. 

,, 24. Alloy with 15 per cent. Sn cooled from fusion. V. x 150 diameters. 

PLATE 7. 

Fig. 25. Alloy with 16 per cent. Sn quenched in liquid air from 160 C. V. x 1000 diameters. 

,, 26. Alloy with 16 per cent. Sn very slowly cooled after prolonged heating. V. x 1000 diameters. 

27. Alloy with 16 per cent. Sn very slowly cooled after long heating,. V. x 1000 diameters. 

28. Alloy with 18 per cent. Sn quenched in liquid air from 160 C. V. x 1000 diameters. 

,, 29. Alloy with 18 per cent. Sn very slowly cooled after prolonged heating. V. x 1000 diameters. 

PLATE 8. 

Fig. 3L Eutectic alloy showing regular lamination. V. x 600 diameters. 

32. Eutectic alloy showing junction of two "grains." V. x 300 diameters. 

33. Eutectic alloy showing junction of three " grains." V. x 300 diameters. 

34. Laminated eutectic alloy. V. x 600 diameters. 

35. Laminated eutectic alloy. V. x 1200 diameters. 

,, 36. Alloy with 64 per cent. Sn. V. x 200 diameters. 

PLATE 9. 

Fig. 37. Alloy with 65 per cent. Sn. V. x 600 diameters. 

,, 38. Segregated eutectic alloy. V. x 200 diameters. 

39. Eutectic alloy showing " spherulitic lustre.' 1 Oblique. x 12 diameters. 

40. Alloy of eutectic composition made by compressing the powdered ingredients. V. x 80 

diameters. 

41. Alloy of eutectic composition from compressed powder. V. x 80 diameters. 

42. Alloy containing 17 per cent. Sn from compressed powder. V. x 80 diameters. 



Rosenhain. 



Phil. Trans., A, To/. 209, Plate 5. 





FIG. 14. 



FIG. 15. 



:^S^S^ 

v=;r- '*="'--''-' ;:v ; ~^' 
~ "^ * '-- i- ~ ^ ~'^'~?*?*^ 










?-lic c !~^- -^~~~-f^ = r^"i --a, ^\ - " 




FIG. 16. 



FIG. 17. 





FIG. 18. 



FIG. 19. 



London Stereoscopic Co. Imp. 




M*i* % 



/%//. Trans., A, Vol. 209, Plate 6. 

., 




V 

5 



-'. '. V r: 



r 






%. 






FIG. 20. 



FIG. 21. 









'-; v ' '.,. 

^~ "f\}<= ^ 



K-*' 



FIG. 22. 





FIG. 23. 



FIG. 24. 



London Stereoscopic Co. Imp. 




Phil. Trans., A, Vnl. 209, Plate 7. 



.** :#y : 



FIG. 25. 



FIG. 26. 




FIG. 27. 





London Stereoscopic Co. Imp. 



FIG. 28. 



FIG. 29. 



Rosenhnin. 



Trans., A, Vl. 209, Plate 8. 





FIG. 31. 



FIG. 32. 




FIG. 33. 






FIG. 35. 



FIG. 36. 








Phil. Trans., A, Vol. 209, Plate p, 





FIG. 4O. 



FIG. 41. 




FIG. 42. 



[ 123 ] 



VI. The Emission and Transmission of Rontqen Rays. 

By G. W. C. KAYE, B.A. (Cantab.), H.Se. (Lond.), A.R.C.Sc., Associate-Member 
of the Institution of Electrical Engineers, Trinity College, Cambridge. 



Communicated l>y Prof. J. J. THOMSON, F.R.S. 
Keceived June 17, Head June 25, 1908. 



OF recent years much interesting work has been done to connect the atomic weight 
of an element with its power of emitting and transmitting various kinds of radiation. 
One may mention McCLELLAND's* work on the secondary radiation given out by a 
substance exposed to the /3 and y rays of radium, and Prof. J. J. TnoMSON'sf results, 
which brought out the relation existing between atomic weight and the intensity 
of the emitted secondary Rontgen radiation. In each case an increase in atomic 
weight was accompanied by an increase in the amount of secondary radiation. 
KLEEMAN J has obtained a similar result in the case of the secondary radiation 
produced by the y rays from radium. 

BENOIST in 1901, working with the absorption by various elements of a definite 
beam of Rontgen rays, obtained a smooth curve approximating to a rectangular 
hyperbola by plotting atomic weight against a factor related to \/p (i.e., the absorption 
of unit mass per unit area), where p is the density of the screen, and X is the coefficient 
of absorption. X is defined by the exponential relation for a homogeneous beam 
I = I e~ A< *, in which I is the intensity of the incident beam, and I that of the emergent 
beam from a layer of thickness d. It follows from BENOIST'S curve that \fp increases 
with the atomic weight, and more rapidly in the region of low atomic weights. 
CROWTHER || measured the absorption by different elements of the j3 rays from 
uranium, and obtained a periodic relation between atomic weight and \/p. 

It was thought that a careful study of the Rontgen radiation emitted by various 

* MCCLELLAND, 'Sci. Trans. Roy. Dublin Soc.,' 1905 and 1906. 
t J. J. THOMSON, 'Proc. Camb. Phil. Soc.,' XIV., 1, p. 109, Nov., 190G. 
J KLEEMAN, 'Phil. Mag.,' p. 618, Nov., 1907. 
BENOIST, ' Journal de Physique ' (3), X., p. 653 (1901). 
|| CROWTHER, 'Phil. Mag.,' p. 379, Oct., 1906. 
VOL. CCIX. A 446. R 2 19.11.08 



124 MR. G. W. C. KAYE ON THE 

elements, when used as anticathodes in a discharge tube, might be repaid by the 
discovery of some sort of relation between their atomic weights and the quantity and 
quality of the Rontgen rays given out and transmitted under various conditions. 

Previous Work. 

It is, of course, known that the heavier metals, or rather, those of high atomic 
weight, make the most efficient anticathodes. RONTGEN* found that the rays from 
platinum are more intense than those from aluminium. CAMPBELL SWINTON! came 
to the conclusion that different metals emit Rontgen rays of the same penetrating 
power and in quantities which depend, but not very much, on the atomic weight. 
KAUFMANN | also showed a rough relation between atomic weight and intensity of 
radiation, and endeavoured without success to find a special connection between the 
rays from a metal and their penetrating power for screens of that metal. R6lTl's 
work should also receive mention. All these observers used a photographic or 
fluoroscopic method of measuring intensities, and to their results can only be attached 
the accuracy which such methods permit. An ionisation method offers obvious 
advantages, and was naturally adopted in the present research. 

Among the work on the transmission of Rontgen rays should be mentioned a paper 
by BENOIST and HUBMUZESCU,|| one by BKNOIST^ in addition to the one referred to 
above, and one by WALTKR.* : ADAMS, ft during the course of the present work, has 
worked on selective absorption, and TlA(4A,JJ during a research on the polarisation of 
secondary Rontgen rays, noticed selective absorption in the case of carbon and ebonite. 
An account of the earlier form of apparatus used by the writer, together with some 
preliminary results on " Selective Absorption," was given in May last year to the 
Cambridge Philosophical Society, 



The central portion of the beam of cathode rays passed down the metal tube T 
(fig. I), and was incident on the anticathode at about 45. A pencil of the Rontgen 
rays produced passed along the tube B, and out through the thin aluminium window 
W, into the ionisation chamber C. Both cathode and anode were of aluminium. 

* RONTGEN, Wiirzburg, Stahel'scher Verlag, Miirz, 1890. 
t SWINTON, ' Proc. Roy. Soc.,' LXI., p. 222 (1897). 
I KAUFMANN, ' Ver. Phy. Ges. Berlin,' XVI., p. 116 (1897). 
E6m, 'Roma R. Accad. Lincei Rendic.,' VI., 2, p. 123 (1897). 
|| BENOIST and HURMUZESCU, 'Compt. Rend.,' Fey. 17, 1896. 
U BENOIST, 'Compt. Rend.,' Jan. 18, 1897. 
** WALTER, 'Ann. der Phys.,' XVII., p. 561 (1905). 

tt J. M. ADAMS, 'Amer. Acad. Arts and Sciences,' XLII., p. 671 (1907); 'Phil. Mag.,' XIII., p. 576 
(1907); 'Phys. Rev.,' XXVL, p. 202 (1908). 

It HAGA, 'Ann. der Phys.,' XXIII., p. 445 (1907). 

KAYE, ' Proc. Camb. Phil. Soc.,' XIV., p. 236, May, 1907. 



EMISSION AND TRANSMISSION OF RONTGEN RAYS. 



125 



A plane cathode was employed so that there was no focussing of the cathode rays ; the 
object was to avoid an undue rise of temperature of the anticathode with the consequent 
liberation of gas. 



TO ELECTROSCO 



EARTH 



CATHODE 




Fig. 1. 

The elements used as anticathodes were mounted in line on ;i ear made of alum- 
inium which ran along horizontal rails fastened by sealing-wax to the bottom of the 
tube A. The rails consisted of one-half of a piece of aluminium tube cut along its 
length from end to end. Underneath each axle of the car was fastened a piece of soft 
iron, and by means of a small electro-magnet outside, the car could be moved and any 
metal desired brought under the beam of cathode rays. 

Anticathodes and Screens. The anticathodes were about 2 cms. diameter, 2 mms. 
thick, and were kept in position by small pins let into the body of the car. Some 
twenty elements w r ere employed as radiators. The metals platinum, tantalum, tin, 
cadmium, silver, palladium, '/me, copper, nickel, iron and aluminium had their surfaces 
cleaned and polished where necessary, first with emery of different grades, and, finally, 
with jewellers' rouge. The lead, thallium, and calcium surfaces were renewed by 
planing or filing immediately before sealing up the tube. The elements bismuth, 
tungsten, antimony, chromium and magnesium were used in the form of powder. 
For these, small trays were spun in a lathe out of thin aluminium sheet, and into 
them the powders were packed tightly, their upper surfaces flush with the rims. 
A disc of gas carbon was used for the carbon anticathode. 

I owe the tantalum to the kindness of Messrs. Siemens and Halske, who were 
good enough to provide me with a suitable specimen. 

Screens of aluminium, iron, nickel, copper, zinc, silver, tin, platinum, and lead were 
employed, and the thickness was in every case determined by weighing. Platinum 



126 MR. G. W. C. KAYE ON THE 

leaf (Q'000025 cm. thick), silver leaf (0'00002 cm. thick), copper leaf (0'000042 cm. 
thick), and aluminium leaf (O'OOOOl cm. thick) were obtained from Nuremberg, and 
were piled for screens of thickness less than about O'OOl cm. Above this thickness 
rolled samples of metal sheet could be procured in most cases. 

The Discharge Tube. The whole anticathode system was earthed and put in 
metallic connection with the anode and the tube T. The discharge was generated by 
a 10-inch Cox induction coil. Across the electrodes an adjustable spark gap, consist- 
ing of two polished brass balls 2'54 cms. in diameter, furnished a rough measure of the 
potential difference, as given by ORGLER'S formula,* 

V = 28,000d, 

where V is the potential difference in volts, and d is the spark length in centimetres. 

A Villard rectifier in circuit prevented reversals of the discharge. The discharge 
tube was connected to a Topler pump, a McLeod gauge, and a P 2 O 5 bulb. 

In the earlier stages of the work a good deal of trouble was caused by the slow and 
steady evolution of gas from the considerable mass of metal in the tube, which 
necessitated much tedious and laborious pumping and delayed the taking of readings. 

In later work a cocoanut charcoal tube which could be surrounded by liquid air 
was mounted on the apparatus, and a barometric mercury cut-off was placed between 
this and the discharge tube. This arrangement enabled the gases which had been 
liberated by the discharge and absorbed by the charcoal to be pumped off at leisure. 

The metal tube T was not present in the earlier form of apparatus, and its intro- 
duction proved of great value in two directions. Firstly, it prevented the excessive 
metallic deposition on the walls of the tube in that region, which formerly unfitted 
the apparatus for use. Secondly, it was employed as a temporary cathode, the other 
electrode being the anticathode system. A tube-cathode concentrates the cathode 
rays along its axis, so that a beam of rays was obtained intense enough to raise the 
point of impact on the anticathode to a white heat in the case of some of the powdered 
elements. By means of a small magnet this point of incandescence could be moved 
about over the surface of the anticathode, and the rate of evolution of the gas in the 
metals was so greatly increased that it did not take very long to reach a state when 
a discharge, using the normal electrodes, caused but little alteration in the vacuum. 

After some weeks' use the bulb lost all inclination to soften and would tend to 
harden considerably during the course of a long run : the absorbed gas would usually be 
expelled again if the bulb were given a rest. Occasionally, too, it would happen that 
one anticathode would harden the bulb, while another would soften it. Platinum, it 
was noticed, almost always tended to harden the tube. After running for an hour or 
so, however, matters would usually adjust themselves, and useful measurements could 
be made if they were taken at definite intervals. The tendency of the bulb to harden 

* ORGLER, 'Ann. der Physik,' I., p. 159 (1900). 



EMISSION AND 'TRANSMISSION OF KONTGEN RAYS. 127 

was largely diminished by using the least current in the primary circuit of the coil, 
which would just cause the discharge to pass in the tube. 

The vacuum could, however, be kept very fairly constant by keeping the apparatus 
joined to the charcoal tube, and disposing and maintaining the level of the outside 
liquid air until a convenient working pressure was arrived at. 

Another and excellent plan, which was latterly always adopted, is to saturate the 
charcoal with gas at the pressure desired, and keep it entirely immersed in the liquid 
air. By this means the pressure can be maintained constant for hours together, no 
matter how intense the discharge. 

In a comparison of the Rontgen rays from different metals it is, of course, essential 
to keep the current in the primary circuit of the coil constant, and an ordinary 
* hammer-break interrupter cannot be relied upon to do this. A mercury turbine 
interrupter working in spirit was used. It proved reliable if periodically cleaned, and 
worked more steadily at high than at low speeds. Any small variations indicated 
by the ammeter in the primary circuit could be followed and corrected for by an 
adjustable resistance. An increase in the current through the primary, besides 
increasing the intensity of the Rontgen rays, has also the effect of augmenting the 
length of the equivalent spark gap of the tube. 

The aluminium window was 0'0065 cm. thick, and 2 cms. in diameter, and 
perceptibly sagged under the outside pressure. It was gripped between two stout 
brass rings screwed together. One of the rings was slipped on to the glass tube B, 
and the joint was completed with sealing-wax. 

The ionisation vessel consisted of a flat cylinder about 9 cms. diameter and 4 cms. 
deep, with its ends covered with aluminium leaf. The middle of the front face was 
about 4 cms. from the aluminium window. A central insulated aluminium ring, over 
which was stretched aluminium leaf, was mounted with its plane parallel to the ends 
of the cylinder. It was insulated by sulphur in an earthed guard tube which was 
mounted in an ebonite plug let into the side of the cylinder. The connection to the gold 
leaf of a Wilson tilted electroscope E (fig. 2) was shielded by earthed tubes. The outside 
of the ionisation chamber was raised by means of a battery of small accumulators, with 
the negative pole earthed, to a potential (200 volts) sufficient to give a saturation 
current for any type of Rontgeii ray. A lead enclosure shielded the electroscope, and 
another surrounded the discharge tube. 

Measurements. 

The very great range in sensitiveness that a tilted electroscope provides was a great 
convenience in the present work, owing to the large variations in intensity of the rays 
dealt with. A potential divider, P, giving a control of a fraction of a volt, was used 
to furnish a fine adjustment on the potential of the charged plate of the electroscope, 
which ordinarily was raised to something in the neighbourhood of 200 volts. 



128 MR. . W. C. KAYE ON THE 

A calcium-chloride solution key, K. which was operated from a distance, made or 
broke the earth connection to the gold-leaf system. 



TO EARTH 




/TO EARTH 

Fig. 2. 

The gold leaf of the electroscope was viewed through a low-power microscope, having 
a scale in the eye-piece. Its time of travel over a definite range was taken with a 
stop-watch, and was usually from 20 to 60 seconds. When things were working well, 
an accuracy of 1 per cent, could he obtained. In a comparison of the radiations from 
a pair of metals, they were used alternately until the readings were concordant. 

Before the merciiry-break was employed, a standard bulb with a platinum anticathode 
was joined in series with the experimental one. It was provided with an ionisation 
chamber and electroscope, and thus served as a check on the constancy of the current 
passing through the two bulbs. But if the mercury-break was working well, the use 
of this standard bulb was not found to be necessary. 

Results. 

The results for the aluminium, copper, and platinum screens will be discussed fully, 
and may be regarded as typical of the rest. 

Of the anticathodes, aluminium, iron, nickel, copper, silver, platinum, and lead 
received special attention. 

Rays direct from Aluminium Window. With a potential difference of 28,000 volts 
on the tube the relative ionisation values for the rays emerging from the aluminium 
window unobstructed by any screen are given in the table below for some of the 
radiators. The value for platinum is made equal to 100. 

These radiation values, although they do not follow the order of the atomic weights, 
divide themselves into four well marked groups Bi to Ta, Sn to Pd, Zu to Fe, and Ca 
to C. The metals of the iron-zinc group are characterised by abnormally high 
radiation values. BARKLA and SADLER,* working with secondary Rontgen rays, have 
arrived at a grouping almost identical, and characterised by similar features, 

* 3ARKLA and SADLER, 'Nature,' p. 344, Feb. 13, 1908. 



EMISSION AND TRANSMISSION OF RONTGEN RAYS. 



129 



Radiator. 


Atomic weight. 


Radiation value. 


Radiator. 


Atomic weight. 


Radiation value. 


Bi 


208-5 


86 


Zn 


65 


79 


Pb 


207 


93 


Cu 


63-6 


89 


Tl 


204 


89 


Ni 


58-7 


90 


Pt 


197 


100 


Fe 


56 


83 


Ta 


183 


110 


Ca 


40 


19 


Sn 


119 


48 


Al 


27 


14 


Cd 


112 


47 


Mg 


24-4 


13 


Pd 


106-5 


49 


C 


12 


5 



STAEKE* measured the relative numbers of secondary cathode particles emitted by 
different metals under the bombardment of a beam of cathode rays. It is of interest 
to compare his results with the corresponding ones of those just quoted. 



Radiator. 


Atomic weight. 


Emitted cathode rays. 


Emitted Rontgcn rays. 


Pt 


197 


100 


100 


Pb 


207 


: 88 


93 


Bi 


208 5 


81 


86 


Ni 


58-7 


67 


90 


Cu 


63 -6 


63 


89 


Fe 


56 


56 


82 


Zn 


65 


56 


79 


Al 


27 


35 


14 


Mg 


24-4 


34 


13 



The order, which is not that of the atomic weights, is, with one exception, the 
same in both cases. The absorption of the softest Rontgen rays by the aluminium 
window probably explains part of the lack of quantitative agreement, especially with 
the radiators of low atomic weight. We have, too, to remember that we are measuring, 
by an ionisation method, the intensities of heterogeneous beams of rays, the components 
of which have very different ionising powers. The general resemblance of the two 
lists is, however, sufficiently noteworthy. 

To bring out any peculiarities in the radiation from any of the anticathodes the 
ionisation values given by the electroscope are taken relative to that of one of the 
metals platinum (which is kept constant and equal to 100 for all screens). These 
relative values are plotted as ordinates against thickness of screen. Thus the graph 
of the platinum radiation is a horizontal straight line, and if all the radiations were 
similar in composition they would be represented by parallel straight lines. 

Figs. 3, 4, and 5 are thus obtained, and show how the Rontgen rays from lead, 
platinum, silver, copper, nickel, iron, and aluminium, generated under a potential 
difference of about 28,000 volts, are dealt with by screens of aluminium, copper, and 

* STARKE, < WIED. Ann.,' LXVL, p. 49 (1898); 'Ann. der Phys.,' III., p. 75 (1900). 
VOL. CCIX. A. 8 



130 



ME. G. W. C. KAYE ON THE 



platinum respectively. The percentage transmitted, of the radiation from platinum, 
is indicated for various thicknesses of screen. 

It ought to be mentioned that the silver anticathocle soon amalgamated with the 
mercury vapour from the pump, and its surface thus became coated with an alloy of 
the probable composition Ag.Hg. 

Aluminium Screens. Consider fig. 3. As the thickness of aluminium screen is 
increased, lead and silver increase their radiation values, and take places warranted 
by their atomic weights. Thus the softest rays due to a lead or silver radiator are 
more penetrating to aluminium than the softest rays from platinum. 



100 




THICKHfSS a, AL 



Fig. 3. Aluminium screen, 28,000 volts. 



The metals of the iron group copper, nickel, and iron rapidly lose, with thicker 
screens, their initially high radiation values. Together with aluminium they afterwards 
show weak maxima at a thickness of about 0'07 cm. of screen. Thus for the range 
0'03 to 0'07 cm. the rays from these metals are more penetrating to aluminium than 
are the rays from platinum, and we thus have a region over which selective 
transmission is manifested, 

It will be noticed that for screens thicker than about 2 mms. an alteration in the 
thickness produces very little change in the relative amounts of radiation from the 



EMISSION AND TRANSMISSION OF RONTGEN RAYS. 



131 



different metals. The inference is that all the beams are now similar in composition, 
and we should therefore be justified in expecting, at this stage, some evident relation 
between intensity and the atomic weight of the radiator. The point is gone into later 
(p. 135), but it may be stated at once that the two are roughly proportional. 

Copper Screens. If we now consider the case of the copper screens (fig. 4), we see 
at once how very different the transmission curves are from those where an aluminium 



I6O 



140 




THICKNESS , 



0025 CM. 
'CU SCREEN - 



0075 



0125 



Fig. 4. Copper screen, 28,000 volts. 



screen was used. As the thickness of screen is increased, silver and lead rise into 
place as before, but iron, nickel, and copper now increase their values and form well- 
marked maxima. Over a considerable range, when anticathodes of copper and nickel 
are used, more radiation emerges from a copper screen than is the case when the 
anticathode is of platinum or lead, although the latter have much higher atomic weights. 

8 2 



132 



MR. G. W. C. KAYE ON THE 



It will be noticed that the nearer the atomic weight of the radiator is to that of 
copper, the more marked and extensive is the maximum. 

The higher the atomic weight, the thicker is the screen at which the peak of the 
curve occurs. The diagram provides a good indication of the amount of radiation 
specially penetrating to copper which is present in each case. The resemblance 
between the radiations from nickel and copper, especially for the thinner screens, is 
noticeable. The case of silver is interesting. As mentioned above, its surface became 



too 




BOOSc. 

THICKNESS or PT SCREEN- 



"OOIO 



OOI5 



O020 



'0025 



Fig. 5. Pt screen, 28,000 volts. 

amalgamated, and hence its radiation could be expected to show features indicative of 
both silver and mercury. This is the explanation of why the graph shows a first 
weak maximum, due to silver, and afterwards rises again owing to the presence of 
the mercury. 

With the thickest copper screens there is every indication that, just as with screens 
of aluminium, the relative values for the penetrating radiations eventually follow the 
order of the atomic weights of the radiators, though even with the thickest screens 
tried the value for the copper radiation is still distinctly relatively higher than with 
the aluminium screens.* 



* This gradual dying away of the selective transmission, as the rays increase in hardness, is in 
accordance with the behaviour of the y rays, which ignore atomic structure. 



EMISSION AND TRANSMISSION OF RONTGEN BAYS. 



133 



Platinum Screens. If we now turn to the transmission curves secured under the 
same conditions with platinum screens (fig. 5), we see in the main a resemblance to 
those obtained with aluminium screens, but with some differences. The radiation 
value for lead is now throughout about 10 per cent, less than that of platinum, but with 
the thickest screens the two curves show some signs of approaching. It is d propos 
to notice here that if screens of lead are used, then the radiation value of lead is 
about 5 per cent, larger than that of platinum for screens of all thicknesses except the 
very thinnest. 

Thus platinum and lead show the phenomenon of selective transmission very nicely. 

With platinum screens the radiation curves for copper, nickel, and iron show very 
flat minima a result consequent on the radiation value of platinum being kept 
constant. Platinum thus shows a not very marked selective transmission over this 
range. Speaking generally, the radiation values with a platinum screen are lower 
than the corresponding ones with an aluminium screen. 

The comparative effect of the three screens -aluminium, copper, and platinum on 
the different radiations is exemplified in the following table. For ease of comparison 
the screens have been chosen of thicknesses which cut down the platinum radiation 
by the same amount in each case. 



Radiator. 


Percentage of radiation transmitted by 








0-17 cm. Al. 


0-008 cm. Cu. 


0-0015 cm. Pt. 




per cent. 


per cent. 


per cent. 


Pt 


2-5 


2-5 


2-5 


Cu 


1-0 


3-1 


0-8 


Ni 


0-98 


1-9 


0-7 


Fe 


0-94 


0-8 


0-6 



Iron, Nickel, and Zinc Screens. Still using the same conditions of experiment, 
measurements of the relative radiations from the different anticathodes were made 
with screens of iron, nickel, and zinc. 

It will be sufficient to say that in each case the curves of transmission are similar 
to those for screens of copper. 

When screen and anticathode are alike or have adjoining atomic weights, the 
radiation is, over a certain region, largely augmented relative to that from any other 
anticathode. The more remote the atomic weights of the radiator and screen, the 
more limited is this region, and the sooner does the anticathode assume a normal 
radiation value, judged on an atomic weight basis. Generally speaking, the lower the 
atomic weight of the radiator in a group, the thinner is the range of screens of like 
metal for which its radiation shows abnormal penetrability. It would seem, therefore, 



134 



MR G. W. C. KAYE ON THE 



that, as the atomic weight of the metal of the screen increases, the harder are the rays 
for which it shows selective transmission. 

General Comparison of Screens. -The following selected values of the relative 
radiations will give a notion as to the degree and extent of the selective transmission 
shown by different screens under the same conditions. As before, the radiations are 
taken relative to that of platinum. 





Al screen. 


Fe screen. 


Ni screen. 


Cu screen. 


Zn screen. 


Pt screen. 


Percentage of ~| 
Pt radiation > 
transmitted J 


9 pei- 
cent. 


2 pei- 
cent. 


9 pei- 
cent. 


2 per 
cent. 


9 pei- 
cent. 


2 per 
cent. 


9 pei- 
cent. 


2 per 
cent. 


9 per 
cent. 


2 per 
cent. 


9 per 
cent. 


2 per 
cent. 


Atomic 


Radia- 


























weight. 


tor. 


























207 


PI) 


105 


107 


99 


104 


100 


102 


100 


102 


100 


101 


88 


86 


195 


Pt 


100 


100 


100 


100 100 


100 


100 


100 


100 


100 


100 


100 


108 




89 


90 


84 


90 79 


90 


82 


88 


80 


90 


67 


64 


63-6 Cu 


39 


34 


45 


41 : 170 


60 


156 


120 


95 


63 


40 


28 


58-7 Ni 


35 


30 


43 


45 155 


55 


120 


75 


80 


39 


33 


24 


56 Fe 


31 


28 


131 


49 72 


33 


80 


32 


50 


25 


24 


22 


27 Al 


19 


12 


22 


15 21 


14 


21 


15 


21 


15 


15 


11 



Apart from the points already mentioned, the most interesting feature is the 
nearness of the radiation values of nickel and copper and the remoteness of those of 
nickel and iron when the thinner of each pair of metal screens is in use. This is 
especially apparent with both thicknesses of the iron, nickel, and copper screens. 
BARKLA and SADLER* working with secondary Rontgen rays have obtained similar 
results and claim a higher value for the atomic weight of nickel than the one usually 
accepted. It should, however, be noticed that with the thicker screens, especially 
those of aluminium and platinum (and it may be added silver and tin), there is a 
distinct tendency for nickel to move into a place justified by its accepted atomic 
weight. It was hoped that light would be thrown on the subject by using a cobalt 
anticathode, but unfortunately the two samples of cobalt used turned out to be 
unsatisfactory and gave much too low a radiation value for all screens. The question 
is referred to later (p. 139). 

The values obtained with silver and tin screens resemble those obtained with 
platinum screens. The very large augmentation in the transmitted radiation when 
screen and radiator are alike is confined to the metals of the chromium-zinc group. 
For other metals the effect is much smaller. 

The general conclusion may be drawn that of all the screens tried aluminium shows 



BARKLA and SADLER, ' Phil. Mag.,' p. 409, Sept., 1907. 



EMISSION AND TRANSMISSION OF RONTGEN RAYS. 



135 



the least anomalous features in its transmission of any of the radiations. It would 
seem, therefore, to be the most suitable material to use in determining the penetrating 
power of a beam of rays. 



Atomic Weight of Radiator and Intensity of Rays. 

It was noticed on p. 130 that for aluminium screens thicker than about 2 mms. very 
little change in the relative amounts of radiation from the different anticathodes is 
caused by an alteration in the thickness of the screen. We are evidently here dealing 
with beams of hard rays of similar composition. 

Under these conditions the intensity of the radiation, from a number of elements, 
was measured, and the values are tabulated below. The liontgen rays used were 
generated under a potential of about 22,000 volts, and a screen of aluminium about 
2 mms. thick was employed; it cut down the initial radiation about 150 times. The 
results are given below ; the radiation values are relative to that of platinum. The 
value for silver is calculated from that of the amalgam Ag. Ilg, using a value for 
mercury obtained from fig. G by interpolation. 



Atomic weight. 
208-5 


Radiator. 


Intensity of 
radiation. 


Radiation 


Atomic weight 


Bi 


112 


0-53 


207 


Pb 


109 


0-53 


204 


Tl 


104 


0-51 


195 


Pt 


100 


0-51 


184 


W 


91 


0-50 


183 


Ta 


90 


0-49 


120 


Sb 


63 


53 


119 


Sn 


60 


0-50 


112 


Cd 


57 


0-51 


108 


Ag 


56 


0-52 


106-5 


PC! 


55 


0-52 


65 


Zn 


35 


0-54 


63-6 


Cu 


33 


0-52 


58-7 


Ni 


30 


0-51 


56 


Fe 


27 


0-48 


52 


Cr 


25 


0-48 


40 


Ca 


16 


0-40 


27 


Al 


11 


0-41 


24-4 
12 


Mg 
C 


10 
5 


0-41 
0-42 



It will be seen that atomic weight and intensity of radiation increase together, the 
latter a little more rapidly than the former. With higher potentials on the tube, the 
metals of high atomic weight increase their radiation values relative to those of the 
In fig. 6 the above intensities are plotted against atomic weight. 



lighter elements. 



136 



ME. G. W. C. KAYE ON THE 



The curve presents some resemblances to those obtained by Prof. J. J. THOMSON* 
when working on secondary Rontgen rays. He also found less difference between the 
amounts of secondary radiation from a metal of low atomic weight and one of high 
when the incident rays were soft than when they were hard. 

To regard the intensity of radiation as proportional to the atomic weight of the 
antieathode is a good rough working rule. The curve has been used to obtain the 
intensities of the radiation for intermediate elements. 













K 

'Tl. 














8 O 








/ 




\GO 






--* 












Po C ' 






^ 












C 












5 




tz.H. 








5 




Jcu. 












If- 












*Cfi. 








K T 


/ 












/C, 













Me.' 












C. 











o -50 100 iso 

ATOMIC WEIGHT or RADIATOR . . 

Fig. 6. 

The list below gives the radia-tion values and the latest determinations of the 
melting points (where known) of those elements which by reason of their refractoriness 
may be regarded as suitable for the antieathode of a focus tube. The physical 
properties of some of them are not convenient, and to others the scarcity and 
consequent price are at present an insurmountable objection. Tantalum is now being 
used in Rontgen bulbs. Its radiation is rather richer than platinum radiation in soft 
rays, and it emits about 10 per cent, less hard rays than platinum. It has the 
advantage of a much higher melting point, and appears not to harden the tubes so 
much as platinum on continued running. All the metals of this group would make 
excellent anticathodes. Generally speaking, the lower the atomic weight the larger 
the proportion of soft rays (or, rather, rays not transparent to aluminium) in the 
radiation. This is especially the case with the metals of the iron group. 

* J. J. THOMSON, ' Proc. Camb. Phil. Soc.,' XIV., 1, p. 109, Nov., 1906. 






EMISSION AND TRANSMISSION OF RONTGEN RAYS. 



137 



Metal. 


Atomic weight. 


Intensity of radiation. 


Melting point. 


Uranium 


238-5 


c. 125 


C. 


Thorium 
Gold .... ... 


232-5 
197 


c. 120 
101 


1064 


Platinum 
Iridium 
Osmium 
Tungsten 


195 
193 
191 

184 


100 

98 
97 
91 


1750 
2250 
2200 
3080 


Tantalum 


183 


90 


2910 


Ytterbium 


173 


86 




Thulium 
Erbium 
Terbium 
Gadolinium 
Samarium 
Palladium 
Rhodium 
Ruthenium 


171. 
166 
160 
156 
150 
106-5 
103 
102 


85 
83 
80 
78 
76 
55 
54 
53 


1350 
1540 
c. 2000 
1900 


Molybdenum 


96 


50 




Niobium 
Zirconium 
Yttrium 


94 
90-6 
89-0 


49 
. 47 
46 


1950 
c. 1300 


Copper 


63-6 


33 


1084 


Cobalt 
Nickel 


59-0 

58-7 


30 
30 


1460 
1430 


Iron 


56 


27 


1500 


Manganese 
Chromium 
Vanadium 
Titanium 


55 
52 
51 

48 


26 
25 

24 
22 


1200 
1490 
1G20 
c. 2500 











Penetrating Powers of tJie Radiations, 

So far attention has been directed more to the relative intensities than to the 
penetrating powers of the different radiations. A new series of experiments was 
carried out with a potential on the tube of about 20,000 volts. The anticathode was 
not changed until a complete set of measurements of the intensity of the rays had 
been made for all the different thicknesses of a metal screen. Figs. 7,8, and 9 are 
derived from the results obtained by inserting screens of aluminium, copper, and 
platinum in the paths of the radiations from aluminium, iron, nickel, copper, and 

platinum. The thickness of screen is plotted against Iog 10 =- , where I is the initial 

-lo 

intensity of the beam as it leaves the aluminium window, and I its intensity after 
transmission through a screen. The slope of the tangent to the curve at any point 
gives (when multiplied by 2'3) the value of the coefficient -of absorption (X.) at that 
region. X is defined by the relation I = I e~* d , where d is the thickness of screen at 
the point. If the relation is homogeneous over any region, the graph will, of course, 
be a straight line. 

VOL. CCIX. A. T 



138 



ME. G. W. C. KAYE ON THE 



Aluminium Screens. Turning to fig. 7 (aluminium screens), we notice a general 
resemblance between the curves for platinum, copper, nickel and iron radiators. They 
indicate the kind of absorption usual with Rontgen rays that is, the coefficient of 
absorption steadily diminishes with increasing thickness of screen. The four curves 
become practically parallel with the thickest screens. The proximity of the early 
portions of the nickel and copper radiation curves will be noticed. 




01 CM. -OZ 

THICKNESS OF A L. SCREE N 



Fig. 7. Al scrcun, 120,000 volts. 

It is the aluminium radiation that presents interest. The curve consists of an 
earlier steeper portion (X = 120) which merges, when the screen attains a thickness of 
about O'Ol cm., into a straight line for the rest of its path (X = 40). Throughout this 
latter region, then, the absorption is exponential, and the aluminium radiation behaves 
as if it were homogeneous. 

Copper Screens. If we inspect fig. 8, which embodies the results obtained with 
copper screens, we no longer see this indication of homogeneity on the part of the 
aluminium radiation. Instead, the curve presents the gradual diminution in gradient 
with increasing thickness of screen that is typical of Rontgen rays. It is now the 
copper radiation that appears homogeneous its graph for screens thicker than about 
G'0015 cm. is a straight line (\ = 470). For thinner screens the curve is a little 
steeper (X = 620). The graph for nickel is very nearly straight over most of its path. 

Iron and platinum yield normal curves like that of aluminium, but have a different 
range of X's. The nearness of the early parts of the curves for nickel and copper 
radiators will again be noticed. It is noteworthy that the radiation from platinum is 






EMISSION AND TRANSMISSION OF RONTGEN RAYS. 



139 



cut down by the thinnest copper screens, more than that from any of the other 
anticathodes. Only for screens thicker than about 0'0045 cm. is the platinum 
radiation more penetrating than that from copper. The platinum curve presently 
crosses the nickel and copper ones, and here the greater penetrating power of the 
platinum radiation becomes apparent. 




THICKNESS * 



Fig. 8. Copper screen, 20,000 volts. 



Platinum Screens. We have noticed the apparent homogeneity of aluminium 
radiation with aluminium screens, and of copper radiation with copper screens, and we 
are led to expect a corresponding result for platinum. It will be seen on inspection 
of fig. 9 that such is the case. While the curves for copper, aluminium, and the other 
radiators are of the normal type, that for platinum is a perfectly straight line (A. = 2350) 
for screens thicker than - 0004 cm. With thinner screens than this, the gradient is 
steeper (A. = 3680). Just as before, the earlier part of the nickel curve lies closer to 
the copper than to the iron curve. 

The regions .corresponding to the maxima in figs. 4, 5, and 6 will be noticed in 
figs. 7, 8, and 9. 

The Atomic Weight of Nickel. Repeated reference has been made (p. 134 and 
elsewhere) to the apparently anomalous behaviour of nickel, and it is here convenient 
to take up the lately discussed question of its atomic weight. BARKLA and SADLER,* 

* BARKLA and SADLER, 'Phil. Mag.,' p. 408, Sept., 1907. 
T 2 



140 



MR. G. W. C. KAYE ON THE 



as mentioned above, claim a higher atomic weight 6 1 '4 for nickel than the value 
587 to which chemists give acceptance. The evidence the latter offer for the atomic 
weights of both nickel and cobalt (59) is so strong, that one hesitates to accept so big 
a change as Messrs. BARKLA and SADLER suggest. Their contention seems to rest on 
the following experiment. The secondary Kontgen radiations from Fe, Ni, Co, Cu, 
and Zn were cut down by a single screen of each of the following metals : Al, Fe, 
Cu, Zn, Ag, Sn, and Pt. The percentage absorptions were plotted against the atomic 
weights of the radiators, and the points for the same screen were joined by a smooth 
curve (fig. 1, p. 410 in their paper). 



2-0 




OOO5".cf, 
TH/CKHESS or PT SCft/V 



Fig. 9. Pt screen, 20,000 volts. 

The curves for five of these screens indicate a value about 61*4 for the atomic 
weight of the nickel radiator ; the curves for the other two screens (Cu and Fe) which 
exhibit selective transmission are not used. It is noteworthy that four of the five 
screens (Al, Ag, Sn, and Pt) have thicknesses which produce roughly the same 
amounts of absorption of the different radiations, so that any anomaly affecting the 
one screen might perhaps be expected to occur with the other three. 

The rest of the paper deals mainly with absorption coefficients and " transparencies." 
These data are calculated from results obtained as above, by assuming the homogeneity 
of the different secondary beams a general assumption admitted by the authors 
themselves to be dubious (p. 421). 

I venture to suggest, on the lines of the results obtained in the present research on 



EMISSION AND TRANSMISSION OF BONTGEN EAYS. 



141 



primary rays, and on the evidence offered by Messrs. BARKLA and SADLER themselves 
(p. 412) as to the homogeneity of their secondary radiations, that such homogeneity 
is only rigidly true when screens and radiator have the same atomic weight or ones 
closely adjoining. If this be the case, the relative absorptions produced by any one 
thickness of a metal screen cannot safely be regarded as characteristic of the radiators ; 
a screen of very different thickness would in general furnish another and a different 
set of relative absorptions. 

Prof. J. J. THOMSON'S* anomalously high result for nickel in his work on Secondary 
Rontgen Radiation can, as he lias pointed out, be equally well explained by 
supposing the radiation value for cobalt to be too low. This would be so if the cobalt 
(which was in the form of fine powder) were partly oxidised ; recently, evidence was 
forthcoming that this was the case. 

The results bearing on the point, obtained in the present work, are suggestive. 
From figs. 7, 8, and 9 (Al, Cu, and Pt screens respectively) mean absorption 
coefficients were obtained from the earliest portions of the curves (i.e., the thinnest 
screens) for iron, nickel, and copper radiations. These are tabulated below : 







liadiator. 












Screen. 


- 








Fo (56). 


Ni (1). 


Cu (03 G). 


Al 


220 


150 


120 


Cu 


870 


690 


620 


Pt 


6800 


5280 


4720 











For each screen the mean X for nickel radiation is nearer the X. for copper than that 
for iron radiation, and each set of numbers plotted against atomic weight gives an 
atomic weight of almost exactly 61 '4 for nickel. 

But if we come to the last portion of the curves and work with thicker screens, and 
in a region which has been shown to be much freer from anomaly than is the case 
with thin screens, then we get different results. With both aluminium and platinum 
screens the absorption coefficients for iron, nickel, and copper radiators are almost 
identical (X about 40 for Al screens, and 3500 for Pt screens). Thus the absorption 
coefficients vary from those tabulated above for thin screens to a practical equality 
for thick screens. The method is therefore useless, at any rate in the case of primary 
rays, to evaluate atomic weights. With copper screens (fig. 8) the final portions of 
the curves are not yet out of the region of selective transmission, but it may be noted 
that the mean absorption coefficients for the thickest screens employed are X = 580 
for iron radiation, 540 for nickel radiation, and 470 for copper radiation a set of 
values which makes nickel perfectly normal. Thus for thick screens, nickel offers no 

* J. J. THOMSON, 'Proc. Camb, Phil. Soc.,' XIV., 1, p. 109, Nov., 1906. 



142 



MR. G. W. C. KAYE ON THE 



anomaly either in the relative intensity of its radiation or in the relative absorption 
coefficients of different screens in dealing with its radiation. 

The anomalous behaviour of nickel with thin screens appears to be due to the fact that 
the softer components of its radiation are considerably more penetrating than the softer 
components of the radiation from iron : possibly also the question of a different distri- 
bution of the rays comes in. If a similar result is true for the secondary radiations and, 
judging from the many points of resemblance between the primary and secondary 
rays from the same metal, such an assumption would not appear to be altogether 
unwarranted then Messrs. BARKLA and SADLER'S results can be completely explained. 

It is worth noticing that KLKEMAN,* working with very hard incident rays (y rays 
from radium), found nickel perfectly normal in the intensity of its secondary radiation. 
liACKETTf measured the quantity of secondary rays produced by the j8 rays from 
radium, and found that nickel took up a place just below cobalt, and one justified by 
its accepted atomic weight. DEWAK and JONES} have recently determined the 
vapour density of nickel carbonyl and confirmed the value 58 '7 obtained by WINKLER 
(1803) and I'rcTiAiiDS and CusHMAN (1890) for the atomic weight of nickel. 




025 

UNIT ARf* C' iCffLV 



125 



Fig. 10. Al radiator, 20,000 volts. 

Absorptions by Equal Masses of Screens.- The interesting feature in the curves of 
figs. 7, 8, and is the homogeneity manifested when radiator and screen are alike. 
Let us examine in turn the way in which the radiations from the metals aluminium, 
copper, and platinum are dealt with by screens of equal masses. In figs. 10, 11, 
and 12, Iog 10 (I/I ) is plotted against the mass per unit area of each of the screens. 

* KLKEMAN, 'Phil. Mag.,' p. 618, Nov., 1907. 
t HACKETT, 'Nature,' 75, p. 535, April, 1907. 
J DEWAR and JONES, ' Proc. Roy. Soc.,' A, 80, p. 234 (1908). 



EMISSION AND TRANSMISSION OF RONTGEtf RAYS. 



143 



2'0, 



; 



1-5 




O25 -05O 
MASS PER UNIT AREA Of SCf! H 



075 







Fig. 11. Copim'. 1 r,-i(li;ilor, 20,000 volts. 

Thus the slope of the tangent at any point on the curves gives (when multiplied by 
2'3) \/p for that region, where p is the density of the screen. The curves in each 
figure indicate the comparative effects of the three screens on the one radiation, and 



15 




-i ,!, i; : : 



1 






CIS 'OSO 
MASS Pf) UAIITAflfA Or C CR H 



Fig. 12. Ft radiator, 20,000 volts. 



144 



MR. G. W. C. KAYE ON THE 



once more display the homogeneity indicated when radiator and screen have the same 
atomic weight, and the lack of it when they are remote. 

As previously mentioned (p. 123), BENOIST,* working with a definite beam of 
Rontgen rays, obtained a smooth curve, hyperbolic in form, by plotting atomic 
weights of screens against " coefficients of transparency " (i.e., the mass of a prism of the 
substance of unit cross-section, which produces the same absorption as a standard 
prism, when the rays travel along the axis). Obviously the transparency (M) is 
inversely proportional to a mean X/p for the region of absorption, for log e (I /I) = 
const, = \d = XM/p. 

BENOIST, using a platinum anticathode, obtained curves which yield the general 
result that X/p increases with the atomic weight of the screen,t and more rapidly in 
the region of low atomic weights : in other words, heavy atoms are more absorbent 
than light, weight for weight. The relative mean values of X/p below are taken from 
his curves to illustrate the point. 







Screens. 






Al (27). 


Cu (64). 


Pt (195). 


Hard rays .... 
Soft rays .... 


4 
10 


36 

75 


100 
100 



If we examine fig. 12 (Pt radiator), BENOIST'S result appears at once from the 
relative slopes of the curves. But, from a general comparison of figs. 10, 11, and 12, 
it is obvious that the shape of BENOIST'S transparency curve, besides depending on the 
extent and region of the absorption, varies considerably with the radiator. As an 
illustration, the relative mean values of X/p for aluminium, copper, and platinum 
screens are obtained from the curves in figs. 10, 11, and 12, and tabulated below for 
the two cases when 50 per cent, and 10 per cent, of the radiation are transmitted. 





50 per cent, transmitted. 


10 per cent, transmitted. 


Radiator. 


Screens. 


Screens. 




AL 


Cu. 


Pt. 


Al. 


Cu. 


Pt. 


Al 


9 


36 


100 


12 


44 


100 


Cu 


19 


27 


100 


17 


30 


100 


Pt 


18 


70 


100 


15 


62 


100 



* BENOIST, ' Journ. de Phys.' (3), X., p. 653 (1901). 

t The statement is also true for the soft y rays from radium. With hard y rays a " density law " holds 
and \/p is constant for different elements. 



EMISSION AND TRANSMISSION OF RONTGEN KAYS. 145 

The fact is clear from the table that for the same radiator \/p is relatively low 
when screen and radiator are alike. With a radiator of copper (or any member of the 
Cr-Zn group) the effect is very marked, and BENOIST'S transparency curve would in 
this case be modified by the addition of a sharp maximum in the neighbourhood of 
the atomic weight of the radiator. BARKLA and SADLER* have obtained a similar 
result in the case of secondary Rontgen rays. With an aluminium anticathode and 
the potential used the transparency curve would be not very far from a straight line. 

The Initial Steepening of the Logarithmic Curves. The early steeper portion of each 
logarithmic curve of transmission when radiator and screen are alike has been noticed 
(figs. 7, 8, and 9). The extent of the steepening depends on the material of the screen. 

An explanation which suggests itself is that the effect is due to the presence, 
in the radiation, of a certain amount of soft rays. If this were the cause, however, we 
should be able to eliminate the preliminary rapid decrease by placing between the 
aluminium window of the tube and the screen a sheet of some other metal thick 
enough to remove all the soft rays. This was tried with several metals, but always 
with the same result. Beyond small changes in the gradients no alteration in the 
shape of the curve was produced, and the kink still remained. In fact, if one 
gradually builds up a composite screen of a number of different metals, the logarithmic 
curve of transmission consists of a series of discontinuous steps made up of an initially 
steep and a subsequently flatter portion for each metal. 

It is clear that the results are not due to the presence of any soft radiation, but we 
can find a ready explanation of the earlier steepness in the curves if we consider the 
effects of secondary radiation. At every stage the primary radiation transmitted by 
a screen is augmented by a certain amount of secondary radiation (in part softer 
than the primary) from the screen itself. For simplicity, let us consider the case of 
homogeneous primary rays. With thick screens none of the secondary radiation 
emerging on the far side of the screen comes from below a certain depth of the screen : 
that proceeding from greater depths is absorbed. Thus, in this region, the transmitted 
primary radiation is increased by a proportional amount of secondary radiation, whose 
presence does not conflict with an exponential law of absorption. But for screens 
which are thinner than this layer, the emergent secondary radiation, not having 
suffered the full absorption, is proportionately larger in amount relative to the 
transmitted primary. Consequently, until the screen attains a certain thickness, the 
intensity of the transmitted radiation will be relatively higher and the curve of 
transmission will be steeper than in the region of thicker screens. 

This explanation is supported by the degrees of abruptness with which the 
steeper parts of the aluminium, copper, and platinum curves (radiator and screen 
being alike) merge into the subsequent slopes. BARKLA and SADLERf have shown 
that with soft primary rays, aluminium emits secondary rays similar to the primary in 

* BARKLA and SADI.EE, ' Phil. Mag.,' p. 416, Sept., 1907. 
t BARKLA and SADLER, ' Nature,' p. 344, Feb. 13, 1908. 
VOL. CCIX. A. <J 



146 



MR. G. W. C. KAYE ON THE 



hardness, but with harder primary rays such secondary radiation is replaced by one 
of a softer type. The absorptive power of aluminium is small, and we should expect 
the change from the steep part of the curve to the rest to be considerable, but 
gradual. This will be seen to be the case in fig. 7, where X gradually changes from 
120 to 40 in a thickness 0'012 cm. of aluminium. 

For copper and platinum the secondary radiations are much softer than the 
primary, and as the absorptive powers of the metals are high, we should expect, as 
figs. 8 and 9 show, a sharp alteration in the slope. With copper, X changes from 
620 to 470 in a thickness 0'0015 cm., while X for platinum changes from 3700 to 2350 
at a thickness 0'0004 cm. 

It is of distinct interest to note that MoOLELLAND,* working on the absorption of 
the /3 rays from radium by metal screens, obtained a similar steepening of his 
logarithmic curves of transmission in their early stages. His results for the ratios 
of the initial to the final slopes in the case of aluminium, copper and platinum are 
tabulated against the present values obtained for llontgen rays. 





Screens. 


Al. 


Cu. 


Pt. 


/3 rays 
X rays 


1-13 
3-0 


1-30 
1-32 


1-58 
1-60 



The agreement with copper and platinum screens is certainly noteworthy. The 
lack of it with aluminium may be ascribed to the abnormal character of its secondary 
Rontgen radiation. 

Effect of the Potential Difference between the Electrodes. The next point investi- 
gated was the effect of a change in the potential difference applied to the terminals of 
the tube, on the apparent homogeneity indicated when screen and radiator are alike. 
Measurements were made at three potentials, about 8,000, 20,000, and 43,000 volts. 
The logarithmic curves of transmission with copper screens and copper and platinum 
anticathodes are given in fig. 13, where the three full-line curves stand for the copper 
radiation, and the dotted curves for the platinum radiation. For ease of comparison 
the initial intensities are made the same at all potentials for each radiator, though 
actually they were very different. It will be seen that the copper radiation is 
transmitted exponentially at both 8,000 and 20,000 volts ; the only difference is that 
a rather lower absorption coefficient accompanies the higher voltage. 

A departure from the exponential law is evident with thick screens in the curve for 
copper radiation at43,000volts. The range of indicated homogeneity becomes restricted, 
and the curve begins to display the features which characterise a normal transmission. 
* MCCLELLAND, 'Sci. Trans. Roy. Dub. Soc.,' IX., p. 25, Feb., 1906. 



EMISSION AND TRANSMISSION OF RONTGEN RAYS. 



147 



The platinum radiation curves should be compared with the ones for copper under 
the same potential difference. An increase in potential lessens the difference between 
the early rates of absorption of the two radiations, and thus minimises the extent of 
the range during which the relative selective transmission of copper radiation by 
copper screens is manifested. 




Fig. 13. Copper screen. 

The curves also indicate the increased intensity (with thick screens) of the platinum 
radiation relative to that of copper which is brought about by iising faster cathode 
rays (see also p. 135). 

Thus the phenomenon of selective transmission shown by a metal depends very 
largely in its extent on the potential applied to the tube. Speaking generally, the 
lower the atomic weight the softer is the class of rays for which a metal exhibits the 
most marked abnormality. 

. Discussion of Results. 

The exponential absorption of Rontgen radiation when radiator and screen are 
alike, the gradual disappearance of such indication of homogeneity with a rise in 
the potential on the tube, and the entire absence of an exponential absorption 
when radiator and screen have remote atomic weights, receive explanation on 
Prof. J. J. THOMSON'S theory of scattering. Scattering may be defined as the tendency 
of a beam, originally parallel, to become diffuse during its passage through a screen. 
Prof. THOMSON has shown (" Conduction of Electricity through Gases," 2nd edition, 

u 2 



148 MK. G. W. C. KAYE ON THE 

p. 405) that the effect of scattering on the transmission of a homogeneous beam is to 
convert an exponential absorption into one in which the coefficients of absorption 
(reckoned on an exponential basis) diminish with the thickness of the screen. The 
larger the ratio of the energy scattered to the energy spent in ionisation of the 
absorbing substance the more will the absorption of the rays depart from an 
exponential law. 

With a coil discharge cathode rays of widely varying velocities are incident upon 
the anticathode. From observations of the magnetic spectrum it appears that a 
considerable proportion of them have a common maximum velocity, at any rate when 
the potential on the tube is not very high. For a large mimber of particles we might 
therefore expect a typical mode of arrest, with, features arising from the corpuscular 
groupings of the atoms of the anticathode. This being so, pulses of a definite type 
peculiar to the metal of the anticathode will form a large part of the Rontgen rays 
emitted. 

It would be expected that pulses thus generated would suffer very little scattering 
on encountering further layers of a metal which presents atomic structures similar to 
those of the anticathode, and that the consequent diminution in intensity would be 
chiefly the result of ionisation. It must be remembered, too, that the rays are sifted 
to some extent before they emerge from the surface of the anticathode. When the 
atoms of the screens provide different corpuscular groupings to those in which the 
Rontgen pulses were generated, then the scattering effect will be pronounced, and 
the law of absorption of the beam would not be an exponential one, even if the beam 
were wholly homogeneous. 

If the potential on the tube is increased, faster cathode particles impinge upon the 
anticathode, harder Rontgen rays are generated, and it will be these which remain 
when the thickest screens are used. Now the importance of the scattering term 
compared with the loss of energy due to ionisation of the absorbing substance 
increases with the hardness of the rays, and we thus have an explanation of why, 
even when screen and radiator are alike, the absorption falls away from exponential 
with higher potentials and thick screens. 

It appears from the results that there is a considerable range in the hardness of the 
rays from an anticathode, for which a screen of the same metal will show an 
exponential absorption. 

The fact that the intensities of similar hard radiations from different anticathodes 
follow the order of atomic weights and not that of densities, indicates for the cathode 
rays encounters which are dependent on the properties of individual atoms, and not 
on their behaviour en masse as a material. With heavy atoms a larger proportion of 
cathode rays would be expected to undergo arrests sufficiently abrupt to produce 
Rontgen rays than would be the case with lighter atoms. 

It is not one of the objects of this paper to discuss the " neutral pair " theory of 
the Rontgen rays recently put forward by Prof. BRAGG, but seems to the writer 



EMISSION AND TRANSMISSION OF RONTGEN RAYS. 149 

that it would be difficult, without some additional and special assumption as to the 
properties of a " pair," to explain on such a theory the marked transparency exhibited 
in the case of both primary and secondary rays when screen and radiator are of the 
same metal. The agreement in the order of the number of reflected cathode particles 
and the intensities of the accompanying Rontgen rays is also to be noticed. 

Summary of Conclusions. 

The primary Rontgen radiations from some twenty elements have been investigated 
under various conditions. 

(1) The relative intensities (measured by an ionisation method) of the radiations as 
they issue from the thin aluminium window of the tube do not follow the order of the 
atomic weights of the anticathodes. Such order shows agreement with that given by 
STAEKE for the relative numbers of cathode rays returned by metallic reflectors. The 
intensities indicate a grouping of the elements which is identical with, and in features 
similar to, that arrived at by BARKLA and SADLER from a consideration of the 
secondary Rontgen rays. 

(2) Over a certain region, when screen and radiator are of the same metal, selective 
transmission of the radiation is manifested, that is, the radiation from the metal is 
augmented relatively to the radiations from other anticathodes. The effect is also 
present to a less extent when radiator and screen have closely adjoining atomic 
weights. With very hard Rontgen rays, selective transmission is only feebly 
displayed. This is in accordance with the behaviour of the y rays which ignore 
atomic structure. 

(3) This augmentation, when radiator and screen are alike, is most pronounced in 
the case of the metals of the chromium-zinc group. It is least marked for a substance 
of low atomic weight such as aluminium, which, of the metals tried, can be regarded 
as the most suitable screen material for measuring ray intensities. 

(4) Speaking generally, the lower the atomic weight of a metal in a group the 
softer is the radiation for which it shows special transparency. 

(5) If the different radiations are cut down by aluminium screens of increasing 
thickness, the intensities reach ultimate relative values which are not altered by a 
further increase in the thickness of the screen. Thus at this stage the rays from all 
the radiators are of the same quality or hardness. These intensity values are 
approximately proportional to the atomic weights of the radiators, and the two, when 
plotted, thus yield, roughly speaking, a straight line. The relative values of the 
heavy-atomed metals increase somewhat with a rise in potential on the tube. Screens 
of other metals eventually yield much the same sort of relation, modified slightly in 
the neighbourhood of the atomic weight of the radiator. 

(6) When screen and radiator are alike, the absorption of unit mass per unit area 
of the screen (in other words, the ratio of the absorption coefficient to the density \/p) 



150 ME. G. W. C. KATE ON THE 

is relatively low. One of the consequences of this is that the shape of BENOIST'S 
" transparency " curve (which indicates that \/p increases with the atomic weight of 
the screen), hesides depending on the range und degree of absorption, is largely 
dependent on the material of the anticathode. For example, the curve is much 
straighter for a radiator of aluminium than for one of platinum, working under the 
same conditions. With an anticathode belonging to the chromium-zinc group the 
transparency curve has to be modified by the addition of a sharp maximum in the 
neighbourhood of the radiator. BAKKLA and SADLER have obtained a similar result 
in the case of secondary Rontgen rays. 

(7) The question of the atomic weight of nickel has been discussed and an 
explanation put forward to account for the anomalous results obtained in connection 
with the secondary radiation from this element. 

(8) The curve of transmission, in which the thickness of screen is plotted against 
the logarithm of the intensity, consists in general of three parts when radiator and 
screen are of the same metal. First, with thin screens there is a relatively steep 
portion, which for thicker screens is followed by a straight-line region : this, again, is 
ultimately succeeded by a region in which the slope gradually diminishes with the 
thickness of the screen. Corresponding to the straight-line portion of the curve there 
is, of course, an exponential absorption. The extent of this region diminishes with a 
rise in the potential on the tube. The preliminary steepening is attributed to secondary 
radiation : in amount, it agrees with that obtained for the same metal by MCCLELLAND 
working with the /3 rays from radium. The ultimate flattening of the curve is 
probably due both to scattering and to the presence of hard rays. This latter region 
may not be detectable if the potential on the tube is not too high, and the absorption 
curve then indicates homogeneity throughout its length. 

(9) When screen and radiator have remote atomic weights, the region of expo- 
nential absorption does not appear. The early portion of the logarithmic curve is 
steepened by secondary radiation, but throughout the whole region the transmission 
is one in which the coefficient of absorption steadily diminishes as the thickness of 
screen increases. This result is probably brought about in the early stages chiefly by 
scattering, and in the later stages by the heterogeneity of the beam. 

In conclusion, it may be remarked, the present research shows that the terms hard 
and soft rays should be confined to comparisons with screens of the same metal. 

It gives me pleasure to thank Prof. THOMSON for his interest in this investigation. 
I wish also to express my indebtedness to Mr. E. EVERETT for his timely and ready 
assistance on occasion. 

Note on the Use of Tilted Electroscopes. As a good deal of time may easily be 
spent in adjusting a tilted electroscope to sensitiveness, it may be permissible to 
mention one or two points in connection with it which I have not seen dealt with 
elsewhere. 



EMISSION AND TRANSMISSION OF RONTGEN RAYS. 151 

The point of support of the gold leaf should not penetrate more than a few 
millimetres within the case of the instrument. A useful length of leaf is 3'5 cms. ; 
the end of the leaf should just swing clear of the charged plate when the instrument 
is tilted on end with the charged plate downwards. 

It should then be found that with the base of the electroscope horizontal, and the 
charged plate at a potential in the neighbourhood of 200 volts, the sensitive region is 
near the middle of the window provided. 

If the charged-plate end of the electroscope be tilted too high, and the potential on 
the plate too large, the leaf will be unstable over a part of its range, i.e., it will not 
return to its zero when earthed. If considerable sensitiveness is aimed at, it is not a 
bad plan to first get the leaf in the unstable condition ; then by means of the adjusting 
screws gradually lower the plate end of the electroscope, and at the same time 
diminish the potential on the plate until the leaf is stable and gives a region with the 
required sensitiveness. The greater the sensitiveness, the more limited the region of 
that sensitiveness an extra volt on the charged plate, or a fraction of a turn of the 
tilting screws, may cause, a large alteration in the sensitiveness. 

With a short leaf, a large potential (240 volts or. more) on the plate and an 
excessive tilt (the charged-plate end very high) will be necessary. A longer leaf 
takes a smaller potential (120 volts or so), and may require a considerable reverse tilt, 
i.e., with the charged-plate end lowest. 

If, when the potential of the leaf is altered, it creeps very slowly and uncertainly to 
its final position, it usually means bad electrical contact between the leaf and its 
support. 



VII. Memoir on the Theory of the Partitions of Numbers. Part IV. On the 
Probability that the Successful Candidate at an Election by Ballot may 
never at any time have Fewer Votes than the One who is Unsuccessful; 
on a Generalization of this Question ; and on its Connexion with oilier 
Questions of Partition, Permutation, and Combination. 

By Major P. A. MACMAHON, F.R.S. 
Received July 15, Read November 19, 1908. 






SECTION 1. 

1. CONSIDEE a lattice in two dimensions, taking, for instance, one in which AB, BC 
are 7 and 5 segments in length respectively. It may be utilised for the study of 
permutations, combinations, and partitions in various ways, also for the study of 
certain questions in the theory of probabilities. 

L I C 



M 



2.* A " line of route " through the lattice from A to may be traced by moving- 
over horizontal segments (a segments) in the direction AB, and over vertical segments 
(ft segments) in the direction BC in any order. Thus one line of route is ADEFGHIC. 
The number of such lines of route is 



or, in general, if AB, BC contain m, n segments respectively, 



\ 



m 



* See "Memoir on the Theory of the Compositions of Numbers," 'Phil. Trans.,' A, 1893. 
VOL. CCIX. A 447. X 27.11.08 



154 MAJOR P. A. MAOMAHON: MEMOIR ON THE 

3. The line of route above depicted denotes a "principal composition" of the 
bipartite number (75), viz., 

(21, 33, TT, 10), 

and, in general, some principal composition of the bipartite number (mn). 

4. It also denotes the permutation 

a'/Sa'jS'ajSa 

of the letters in the product a 7 ^ 5 ; and, in general, some permutation of the letters in 
the product M y3 n . 

5. The line of route divides the lattice into two portions, each of which denotes the 
Sylvester-Ferrers graph of a partition of a unipartite number. 

Consider, for example, the portion of the lattice bounded by ADEFGHICB. We 
obtain the graph of a partition in two ways : 

(i) By placing a unit (or node) in the centre of each square contained in the 

bounded area ; thus 

1 

11 

11 

11 

11111 

denotes the partition 54111, or its conjugate 52221 of the number 12. 

In general, we thus obtain a partition of some numbers into n, or fewer, parts, the 
part magnitude being limited not to exceed m, and its conjugate a partition of some 
numbers into m, or fewer, parts, the part magnitude being limited not to exceed n. 

Similarly the remaining portion of the lattice denotes some partition and its 
conjugate. 

(ii) By placing a unit (or node) at the centre of each segment to the right hand of 
the points A, E, J, K, G, I respectively ; thus 

1 

11 
11 
11 

11111 
1111111 

denotes the partition 6522211, or its conjugate 752221 of the number 19. 

In general, we thus obtain a partition of some numbers into m parts, the part 
magnitude being limited not to exceed n+1, and its conjugate, a partition having m 
for the highest part, the number of parts being limited not to exceed n+1. 

The remaining portion of the lattice may be similarly interpreted. 






THEOEY OP THE PARTITIONS OF NUMBERS. 155 

6. The line of route also denotes the zig-zag graph of a composition of a unipartite 
number. 

For placing nodes at all points passed over by the line of route we obtain 




. . r 





the graph of the composition 341122, and also of three other compositions 

221143 

12411211 

11211421 

of the number 13. (See ' Phil. Trans.,' Series A, vol. 207, pp. G5-134.) 

In general, we thus obtain four compositions of the unipartite number m + n+l. 

It will thus be noted that these four compositions of a unipartite number define two 

pairs of partitions of unipartite numbers, and clearly every theorem in partitions can 

be made to give a corresponding theorem of compositions. 

This manifold interpretation of the line of route through a lattice must be borne in 

mind throughout the following investigation. 

7. My object now is to show how certain questions of probability can be treated by 
means of the lattice. 

BERTRAND and DESIRE ANDRE* have discussed a question which they have stated 
in the following terms : 

" Pierre et Paul sont soumis a un scrutin de ballottage ; 1'urne contient m bulletins 
favorables a Pierre, n favorables a Paul ; m est plus grand que it,, Pierre sera elu. 
Quelle est la probabilite pour que, pendant le depouillement du scrutin, les bulletins 
sortent dans un ordre tel que Pierre ne cesse pas un seul instant d' avoir 1'avantage ?" 

The probability is found by an ingenious method to be 

m n 

m+n ' 

8. I discuss the question by drawing in the lattice the line AL,t making an angle 
of 45 with the line AB. The problem of BERTRAND and ANDRE is seen to be 

* 'Calcul des Probabilites,' par J. BERTRAND, Paris, 1888. J. BERTRAND et D. ANDRE, 'Comptes 
Rendus de 1'Academie des Sciences,' tome cv., p. 369 et 436, Paris, 1887. 

t " Theories des Nombres," tome 1, par EDOUARD LUCAS, ' Le Scrqtin de ballottage' (pp. 83, 84, 164). 

x 2 



156 MAJOR P. A. MAcMAHON: MEMOIR ON THE 

identical with that of enumerating the lines of route which neither cross nor touch 
the line AL, for each such line of route gives a permutation tf the letters in a m y8" 
which is required by the conditions. 

I prefer in the first instance to alter the conditions of the problem so as to 
determine the probability that Pierre never at any instant has fewer votes than 
Paul. The lines of route to be enumerated are then those which do not cross, but 
which may touch the line AL. 

Owing to the different interpretations that may be given to the line of route many 
courses of procedure are open. I select that one which in the special graphs gives the 

partition 

752221 

and, in general, a partition having TO for the highest part and a number of parts not 
exceeding n+l. 

Regarding zero as au admissible part, let the parts of such a partition be (in 
descending order) 

,, 2 , ... n + 1 . 

These parts are subject to the conditions 



a, > a 3 2 , 

i> 3 + 2 (,,), 

.f S: 4 ( 4 ), 

!2:a4 + 3 (a s ), 

<- ! 2: - (t(w-t), 

*1 2: Ot n ,-\-n' 1 (2n'-3J, 

where 11! = n+l. 

We can perform the summation 

^'Za*... #,"' 

for all numbers satisfying the above 2// 3 conditions. 
9. Suppose n = 3, the sum in question is 



a, 



the meaning of the symbol | being that, after expansion in ascending powers of 

Xj, x 2 , x 3 , all terms involving negative powers of a lt a 3) a 3 are to be rejected, and that 
in the surviving terms a lt a 2 , a 3 are, each of them, to be put equal to unity. 

* See "Memoir on the Theory of the Partitions of Numbers, Part II,," 'Phil, Trans.,' A, vol. 192, 
1899. 



THEORY OP THE PARTITIONS OP NUMBERS. 157 

The quantity 2 is at once eliminated and we obtain 



fl 



1- X 

a, 
a 3 is now easily eliminated and we obtain 



i 
To eliminate i we require the easily established theorem 



1 1 x . lxy 

11 J 

c 



Thence we reach the final result 



\.i\. 1 .7X2- 1 .'VV:/ 

which shows in the clearest possible manner how the partitions are constructed. The 
denominator factors indicate that we may write do\vn any partition composed of three 
parts ; the numerator terms xf, .i\ 2 .c 2 show that we may add either '2 to the first part 
or simultaneously 2 to the first and 1 to the -second part. We in that manner obtain 
every partition satisfying the conditions, but the numerator term .f.yV 2 shows that 
certain partitions are in this manner obtained twice over. 

10. As we are only concerned with the magnitude of the highest part and not at 
all with the weight of the partition, we may for the present purpose put Xi = x, 
%2 = 3 = 1, and consider the result 



(I-*) 3 
as the one to generalise. 

11. I write down the expression 



~' 2 ~ 3 



y 1 ( * 2 1 a * 1 ( ^ 1 ^2'-4 1. 

. . ,a 2n _ 3 x . i . i . i . ... i . i 



as the crude expression for the sum. 

We can immediately eliminate all the auxiliaries a which have an even suffix and 
reach the expression 



. 11 

1 a t 3 a 6 . . .a 9H - 9 c .1 .1 -.1 



15 8 MAJOE P. A. MAcMAHON: MEMOIR ON THE 

We now require the auxiliary theorem 

n _ <L _ 



cx l .1 -- x 2 . 1 -- x 3 . . . 1 -- x p 
c c c 



1 X l . 1 X&2 . I XiX-s , . . . 1 

so that, eliminating a lt we reach 



-a-, 



and, eliminating 3 , 



2: (l-a 5 ci 1 ..Mw-- J x) 3 (l-a 1 ...a. M - s x)...(I-a 2n .- 3 x) (l-x)' 

Note that for n' = 3 or /6 = 2 this becomes the before obtained expression 

2x 2 -x s 
Ij-xf 

To eliminate S) we have to substitute for 



(1 a 5 a 7 ... 

the expression 



.r' 



(Y-a b a.,...a, n .-sxf 
and then put a- a = 1, thus getting 

2dj "t^9 '.../2' 5 ^2n' o ( *5^^7 '('Jn' 3'^' OCfj . t-1j 2ii'&*' "l CJ&y ,..^2' 3^ / *^ 

as the expression to be substituted for 
in the numerator, which thus becomes 



This, for ?-' = 4 or w = 3, is 
which may be written 



THEORY OF THE PARTITIONS OF NUMBERS. 159 

in a form showing its mode of derivation from 



(l-xf 

We now see that, when n' = p+ 1, we get a form which may be written 



and then, when n' = p + 2, the form is 



where the numerator of the function last written is 



Hence 



ip+l\ 
= r 2 }u pl -u p3 , 



= (p +l 



U 



P+1,P~1 ( t,_]J llpltlpp , 



\p 
I 



These relations are satisfied by 



2p 
v 2-1 J\l 

so that the result of the summation is 



> ( 

pq ~p\ <z-i / \p-qj' 



n 







\fn\f 2n\ +1 1/n+lW 2n \ +2 , y lf2n-2\f2n\ ^ 

'- 1 -'* f n\ 2 yU-sj* ( >n(n-i)(or 



and there is no difficulty in showing that this in fact is equal to 

-l\ 



160 MAJOR P. A. MAcMAHON: MEMOIR ON THE 

12. Hence the number of partitions having a highest part m and n+l parts, zero 
being included as a part, subject to the given conditions as regards magnitude is 

fn + ml\ _ fn + ml 
( n J ( n-2 

which may be also written 

m n+ 1 /m+n\ 

m+l \ m )' 

This, therefore, is the number of lines of route which do not cross the line AL. 
Hence the probability that Pierre is never in a minority is 

mn+l 
m + I 

13. From this probability, which call F (m, n), is immediately derivable the 
probability disciissed by BERTRAND and ANDRE, which call P (m, n). 

For in the lattice - - is the probability that the line ol route passes through the 

point M, and thence we find 

p / \ m T7 { \ m ~ n 

m + H m + n' 

Other probability questions may be discussed in a similar manner, with the 
advantage that light is at the same time thrown upon several other problems of 
partitions, compositions, and combinations of unipartite and bipartite numbers. In 
the above investigation we have had before us partitions of unipartite numbers which 
have a given number of parts, a given highest part and parts which in addition satisfy 
certain inequalities. 

14. If we had had before us the parallel theory of the compositions of unipartite 
numbers there would have been the composition 

in correspondence with the partition 



the weight X/3 and the number of parts n would have been given and the parts 
^8,, ft?,... would have been subject to the inequalities 

A 2= 2, 



A 



THEOEY OF THE PARTITIONS OF NUMBERS. 161 

In the former case the partitions of highest part m and n parts (zero not excluded) 
are enumerated by 

mn + 2 /m + n 
m+l \ m 

In the latter the compositions of the number w, having n parts (zero excluded 
because ft n = +!), are enumerated by 

w 2n+2 /wl \ 
w-n+1 \n-IJ' 

Ex. gr. for w = 6, n = 3, we have the five compositions 

411 

321 

312 

231 

222 
which satisfy the given inequalities. 

In this Section I have shown the connexion between a well-known question in 
probabilities and varioiis other combinatorial questions in preparation for the 
generalization to which I now proceed in Section 2. 

SECTION 2. 

15. In the Second Memoir on the Partitions of Numbers I broached the subject of 
the two-dimensional partitions of numbers. I start with any Sylvester-Ferrers graph 
of an ordinary one-dimensional partition say 



and I consider the parts of the partition to be placed at the nodes in suchwise that 
the numbers in the rows, read from West to East, and also in the columns read from 
North to South, are in descending order of magnitude. Thus 

433222 

3222 

2111 

21 

2 

is a two-dimensional partition of the number 35. 
YOL, ccix, A. T 



MAJOE P. A. MAcMAHON: MEMOIR ON THE 

The Memoir referred to contained some striking results in the theory, but the 
general result as conjectured and verified in numerous instances remained unproved. 

The present paper is mainly concerned with the partitions into different parts 
placed at the nodes of any graph, and with the associated question in probabilities, a 
generalization of that of Section 1. 

Taking any graph of n nodes and any n different integers, the inquiry is as to the 
number of ways of placing the numbers at the nodes so that the descending orders in 
the rows and columns, as above defined, are in evidence. 

Consider in detail a simple case that of six different numbers at the nodes of 
the graph 



We find the 16 arrangements 



(554 


654 


653 


653 


652 


652 


651 


651 


32 


31 


42 


41 


43 


41 


43 


42 


1 


2 


1 


2 


1 


3 


2 


3 


631 


632 


641 


642 


641 


643 


642 


643 


52 


51 


52 


51 


53 


51 


53 


52 


4 


4 


3 


3 


2 


2 


1 


1 



the second row of eight arrangements being the conjugates of those in the first row 
because the graph is self- conjugate. 

16. The problem is immediately transformable into one concerned with the 
conditioned permutations of the six numbers in a line. 

Take the form 

654^ 

32 * 



;t 



and suppose the six numbers to be written down in a line so that four descending 

orders 

654^ 

32 -* 
631* 

52 * 

are in evidence ; I say that there is a one-to-one correspondence between such 
permutations and the two-dimensional partitions under investigation. 
To see how this is, take any one of the 16 arrangements 

632 

51 

4 



THEORY OF THE PARTITIONS OF NUMBERS. 



1G3 






and taking each number in succession, in order from the highest to the lowest, write 
a letter a, /3, or y, according as the number is in the first, second, or third row. Thus 
beginning with 6 we write down a, then for 5 ft, for 4 y, for 3 a, for 2 a, and, lastly, 
for 1 ft, thus obtaining 

a , ft, J, , , ft- 

Now underneath the a's write G, 5, 4 in order, under the ft's, 3, 2 in order, and 
under y 1, in accordance with the rows of the arrangement 

654 

32 

1 



We thus obtain 



I say that 



a ft y a. a ft 

G 3 1 5 4 2. 

631542 



is a permutation subject to the given conditions as defined by the descending orders 

in the arrangement 

654 

32 
1 

The 16 permutations corresponding to the 16 graph arrangements are 



aaappy 
654321 

a.a.ftftya, 
653214 



aaapyp 
654312 



act.fta.fty 
G53421 



a,a.fta.yft 
653412 



a.aftfta.y 
653241 



aa.ftya.ft 
653142 



aaftyfta aftyafta aftyaaft aftayfta aftayaft 
653124 631524 631542 635124 635142 

aftaftya. aftaayft aftaftay aftaafty 
635214 635412 635241 635421. 

To show that there are no other permutations it is sufficient to prove that one can 
pass back from a permutation to a graph in a unique manner. 

Thus take the permutation 

635124; 



write a's under 6, 5, 4 ; /3's under 3, 2 ; and y under 1 : 

635124 



the succession 



ctftctyfta. 
Y 2 



164 MAJOR P. A. MACMAHON: MEMOIR ON THE 

indicates that 6 is in the first row corresponding to a, 
5 second /3, 
4 ,, first ,, ,, ,, , 
3 third y, 
2 second ft, 
I first . 

Hence the arrangement 

641 

52 
3 

The transformation is quite general ; thus from 

12 9 7 4 
11 8 6 2 

10 5 3 1 

we pass to 

a fl y a /8 /8yy/3y 

12 8 4 11 7 10 6 3 9 2 5 1, 
a permutation in which the descending orders indicated by 

12 11 10 9 
8765 

4321 
are in evidence. 

17. The first question is the enumeration of the partitions where the graph and the 
set of unequal numbers are given. 

Let the graph contain a, b, c, ... nodes in the successive rows, and for a given set 
of a + b + c+... unequal numbers, let 

(abc...;) 

denote the number of partitions. 
Observe that above we found 

(321 ;) = 16. 
First we note that 



*Next take a graph of two rows. In any such graph 



Compare " Probleme des deux files de soldats," ' Theories des Nombres,' tome 1, p. 86, par EDOUARD LUCAS. 



THEORY OF THE PARTITIONS OF NUMBERS. 165 

if c be the smallest number involved, the arrangements are of two types, viz., 

c 

or 

6 

except when the rows contain the same number of nodes ; then there is the one type 



e 

Hence, a moment's consideration establishes the relations 

(a, 6-1;) 



when a > b, and 

(aa;) = (a, a- 1 ;). 

Treating these as difference equations it is easy to obtain the result 

> (a + M! / 7 , i\ /a + b\ab+l 

;) = /-* - \-r-n ( a -v + l ) = \ - r~ > 

(a+1)! 6P \ a / a+1 

, x (2) ! /2a\ 

(; '~a+i!! = 



18. This case of two rows is worth a special examination before proceeding to a 
greater number of rows. First consider the generating function of the numbers (aa ;) : 

u x = 1(aa;}x a = I 
If we expand 

( 

we find that the general term after the first is 



and thence 

^ = 

and 

xUf 

exhibiting a remarkable property of u x . 
Reverting to the difference equation 



= 0, 



(aa;) = (a, a-1;) 

= (a, a-2 ;) + (a-l, a 1 ;) 

= (a, a-3;) + 2(a-l, a-2;) 

= (a, a-4 ;) + 3 (a-1, a-3 ;) + 2 (a-2, a-2), 



1(50 MAJOR P. A. MACMAHON: MEMOIR ON THE 

and observing that this last result may be written 

(aa;) = (40;) (a, a-4;) + (31;)(a-l, a-3 ;) + (22 ;)(a-2, a-2;), 
it is natural to suspect the law 

(aa ;) = 2 (at ;) (a-t, a-s ;), 
where 

s + t = constant, 
and it is easy to establish it. 

For consider the graph 





The four lowest numbers at the nodes are 

(i) The last four of the second row, 

(ii) The last of the first row and the last three of the second, 

(iii) The last two of both rows. 

Taking case (ii), the nodes marked x, the numbers may be 

234 

431 or 421 or 321, 

and these arrangements are enumerated by (31;), we see, by subtracting each number 
from the number 5. Hence, in particular, 

(88 ;) = (40 ;) (84 ;) + (31 ;) (75 ;) + (22 ;) (66 ;), 
and, in general, 

(;) = (at;) (a I, as ;) where s + t constant. 



19. Representation of (aa ;) as a Sum of Squares. 
Putting s + t = a, we find 

(aa;) = (aO;) 2 +(a-l, 1 ;) 2 +(a-2, 2 ;) 2 + ..., 

the last term being 

(|a,-|a;) 2 or {(+!), i( a - 1)} 2 , 

ascending as a is even or uneven. 
Hence the identity 



THEORY OF THE PARTITIONS OF NUMBERS. 167 

the last term of the series being the square of 

a\ c 2. a! 

or of 



ascending as a is even or uneven. 

The permutations enumerated by (aa ;) are those of 2a numbers 



all different and subject to a + 2 descending orders corresponding to the a columns 
and the 2 rows. 

20. Consider now other permutations such that whilst the row numbers are in 
descending order, exactly s of the a column pairs are not in descending order. 

Let (aa ; s) be the number of such permutations. I propose to show that 

(aa ; .s-) = (aa ; 0) = (aa ;) 

for all values of s, from ,<? = to ,s = a. 
Ex. gr., the permutations enumerated by 

(22 ; 0) are 43 42 
21 31, 

(22 ; 1) are 41 32 

32 41, 

(22 ; 2) are 31 21 
42 43. 
To establish this theorem, since 



and 

xu z 2 = u z l, 
we find 



(aa;) = (a-1, a-l;) + (a-2, a-2 ;) (11 ;)+ ... + (11 ;) (a-2, a-2;) + (a-l, a-1;). 

The right-hand side of this identity is equal to 

(aa; I), 

for it consists of a terms, of which the first enumerates the permutations in which the 
pair m^n^ is out of order, the second those in which the pair m 3 n a is out of order, and 

so on. Hence 

(aa;) = (aa ; 1). 



168 MA JOE P. A. MAcMAHON: MEMOIR ON THE 

Consider in general the arrangement 



where the a pairs are in order and the /3 pairs out of order. 
For this particular arrangement the enumeration is given by 



Put 

u z = 1 + X, 



The generating function to be considered is 

1 + X+Y + XY + YX + XYX + YXY+XYXY+YXYX+.... 

The X, Y in a product occurring alternately in all possible ways. 
This function is 



1-XY 

or 



or 

xn x yu y 

x-y 
since 

xu x a u x +l = yUy 2 -Vy+I = 0. 
Now 



x ~~y 

and the coefficient of x"~*?/* in the function is none other than 

(aa ; s). 
Hence 

(aa ; s) = (aa ;), 
a remarkable theorem. 

21. I will now obtain the generating function for the numbers (ab ;). Since 



, 
a a+l 

& Wi / -ii(' 
\ a / o i \ a 



THEOKY OF THE PARTITIONS OF NUMBERS. 169 

As yet we have assigned no meaning to (ab ;) when a < b, but retaining such terms 
and adding to the term 

ry 



terms given by placing a equal to zero, we obtain the suggestive redundant 
generating function 



X 



\-x-y 
in the expansion of which we require only those terms involving 

scY 

in which a 2t 1). 

To eliminate the terms containing x~ l we have merely to add 

y 

X , 



and then we obtain 

l-2y 



l-y, l-x-y 

We might also seek to remove those terms in x a t/' for which a < b, but for my 
present purpose the redundant form is quite as convenient and infinitely more 
suggestive. * 

22. The result 

/a + b\a b+l 
= a 



leads to the observation that the number obtained is precisely that obtained in 
Section 1 for the number of arrangements of the letters in 



a." 



such that drawing a line between any two letters the number of a's to the left of the 
line 2: to the number of )S's to the left of the line. Also that 



is the solution of the probability question for a + b electors. 

The one-to-one correspondence is easily established, for suppose 



* 



86531 

742 



I have found that the reduced generating function is 



ix y 
VOL. CCIX. A. Z 



170 MAJOK P. A. MAcMAHON: MEMOIR ON THE 

is an arrangement enumerated by (53 ;), I take the numbers 8, 7, 6, 5, 4, 3, 2, 1 in 
descending order and write down a when the number is in the first row and /8 when 
it is in the second, thus 

87654321 



and we now have an arrangement of the letters in 

6 /8 3 

such that, proceeding from left to right and stopping at any point, the number of a's 
met with is at least as large as the number of yS's. 

The result and correspondence are at once generalisable, for consider the arrangement 

9765 

832 

4 

1 ; 

we are led to the permutation of 4 y6 3 yS, viz., 



which is such that, in passing from left to right, we have at any instant 

(i) passed over at least as many a's as /3's, 

(ii) ,, 's y's, 

(iii) y's S's. 

Hence, if in an election four candidates have a, b, c, d (these numbers being in 
descending order of magnitude) supporters respectively, and at any instant they have 
respectively A, B, C, D votes, the probability that always 



s 



and, in general, if the votes polled at any instant show invariably the final order of the 
candidates, we have a state of affairs of which the probability is 



23. From the result 



(abode... ;) - ( + b + c + d+e + ...)\ 
V alblc\dle\... 



THEORY OF THE PARTITIONS OF NUMBERS. 171 

/ 

we find the analytical results 

(a-l,a;) = 0, 

(6-1, + !;) = -(&;), 

and the latter of these is not so far interpretable. 
Passing to three rows 



containing a, b, and c nodes respectively, it is seen that the smallest of the 
different numbers must be situated at the right-hand nodes of some row, unless such 
row contains as many nodes as the row beneath. 
Hence the difference equation 

(abci) = (ft- 1, b, c;) + (a, b-l, c ;) + (ft, b, c-1 ;), 
provided that (abc ;) = when either 

ab+l = or bc+1 = 0. 
I find such a solution of the difference equation to be 



This is only interpretable when 

a > b > c , 
but analytically 

+ (abc;) = +(b-l,c-l,a + 2;)= +(c-2, a+ 1, b+ 1 ;) 
= -(a, c-1, 6+1;)= -(&-!, a+l,c;) = -(c-2, b, a + 2 ;), 

relations which are useful for the manipulation of the functions. 
The sum 



with the inclusion of redundant terms I find to be 



x y x 



l-x-y-z 

an expression which is remarkably suggestive. 

z 2 



172 MAJOR P. A. MAcMAHON: MEMOIR ON THE 

To establish the expression it is merely necessary to verify that the coefficient of 



, vz. : 



_ 
c\blcl (a+l)!(6-l)!c! a! (6+1)1 (c-1)! 



c)\ (a + 6 + c)! __ (a + 6 + c)! 

(a+2)! (6-1)! (c-1)! (o+l)! (6+1)! (c-2)! (a+2)! 6! (c-2)! 

reduces to the value of (6c;) above given. 

This is easy because it appears at once that a 6 + 1, 6 c+1, and a c + 2 are 
factors. 

It is easy now to conjecture the form of the general result. 

The truth of the generating function for (abc;) is, perhaps, best seen by writing 



6+1/V a + 2/' 



where ( ) stands for ' J- . 

\ a, 6 / a ! 6 ! c ! 

24. I will now establish the result 



x fi L-i_ > i 



_L_l--- l- 

" 



f 1 '-fn 1 \ / i ^n 

X 1 - 



by showing that this expression satisfies the difference equation 
(a,,a 2 , a s , ...;) = (i-l, a 2 , 03. ..;) + (a 1; a a -l, a s , ...;) + ... + ( 
Writing the co-factors of the multinomial coefficients in 

(a,, a 2 , a 3 , ... a n ;) and (a 1( a 2 , ... a,-l, ... a n ;) 
as 

C and C, respectively, 






THEORY OF THE PARTITIONS OF NUMBERS. 173 

we find 



2 + a 3 C 3 + . . . 4- a n C H . 
To prove this relation I will show that any factor 



1 -- _(><) of C 
a t +s t^ 

is also a factor of 

2 + . . . + a n C a . 



First observe that 1 -- - is a factor of CL unless m is equal to s or t 

. a t + st 

Therefore consider merely 

a t C t +a,C t . 

The factors of C which involve either a t or a s or both a, and a t are 

,. \m = t-\ I n \m=s-lf -. ,, = n / 

i -- = ] n (i -- ^ ) n (i -- ^ n i 



,=i \ a m + s TO/ ,=+i \ a m + sm/ P =, 

q=-l / 

n i n i n i 



Hence, disregarding a common factor, C t involves the factors 

a t a,+s t l'"^ l a m a, + s m m= ^' l a m a s + s m p =" a s a p s+p 
a t + st l =i a m +sm m =t+i a m + sm /)= +i a s s+p 



1=1 di + tl ?=s +i a t + q t 1 ?=<+! 
and C, involves the factors 

a t a, + s t+l m= ^~ l a m a s +s m+l " l= ^ l a m a s + s m+l ^" a, a p +p s 
t m =i a m + sm m =t+i a m + sm P = s +i a t +psl 



i=\ ai + tl q= s +i a t t + q q=t+i a t t + q 

Discarding common factors from these expressions we find that C t involves the 
factors 



. _ 

a t +s t 1 a,s+n 



*n 
x ( 



a t +s-t a t 



174 MAJOE P. A. MACMAHON: MEMOIE ON THE 

and that C s involves the factors 



( ]( _ t] a^a 

a 



a, 



. 

a t t+n a t + stl 



vt f v ) in ^^t I " ** - 1 - 

Hence a t C t + a,C, involves a factor which by elimination of a t by means of the 
relation 

1 ^ = 

a t +s t 

may be written 

( 1) ((_! a s + n t-+ 1) (a,_i a s + 1) (o s s + ti) (! , + } (a, a s+1 ) (a, a (+1 s + <) 






and this is at once seen to be zero. Hence 



contains 

1 2t_ (s>t) 

a t +st 

as a factor. It therefore contains C as a factor. 

It also contains another factor which is linear, and considerations of symmetry 
show it to be 



Hence the expression assumed for 

satisfies the difference equation, and is evidently the expression corresponding to the 
problem in hand. 

25. We now observe that a redundant generating function, viz., an expression for 
the sum 

^? / /-j /v // ft \ /y ^i /y ^"2 ^y* ^3 o "* 

^t^]j ^2* ^3) n )/ *^1 *^2 "^"3 * *^n j 

is 

n" ( n"Yi--^ 



=t+l t=l \ X 



l (x 1 + x 2 +x a +...+x n ) 

The question in probabilities, here, I believe, solved for the first time, may be 
stated as follows : 



THEORY OF THE PARTITIONS OF NUMBERS. 175 

If n candidates at an election have 

1, 2, 3, <* 

voters in their favour respectively, where 



and if any instant A 1} A 2 , ... A B _ l5 A B voters have recorded their votes in favour of 
the several candidates respectively, the probability that ahvays 



s 

s=n tn 



n n (i ^ 



(=1 



The interesting point is the connection of the problem with the theory of the 
two-dimensional partitions of any set of 2 unequal numbers. 

The graph solution proves at once the remarkable theorem that if (bJ>J) s ...) be the 
partition conjugate to (a^cis...), 



a fact which it would be difficult to establish by pure algebra. In this case the 
corresponding probabilities are in the inverse ratio of 



2 +a s +...)l 






[ 177 ] 



VJII. On the Osmotic Pressures of Aqueous Solutions of Calcium Ferrocyanide. 

Part I. Concentrated Solutions. 

By the EARL OF BERKELEY, F.R.S., E. G. J. HARTLEY, B.A. (Oxon.), 
and C. V. BURTON, D.Sc. (Land.). 

Received July 4, Read November 5, 1908. 

IN the following communication the experiments on the direct measurement of the 
osmotic pressures, on the vapour pressures, and on the densities have been carried 
out in conjunction with Mr. E. G. J. HARTLEY, those on the compressibilities with 
Dr. C. V. BURTON. 

In the 'Proceedings of the Royal Society,' Series A, vol. 77 (1906), pp. 15G-1G9, 
Mr. HARTLEY and I gave a preliminary account of the determination of the osmotic 
pressures of strong aqueous solutions of cane sugar by means of measurements of the 
relative lowering of their vapour pressures as compared to that of water. We deduced 
a formula for the connection between the vapour and osmotic pressures of a solution, 
which, in view of the experimental errors, justified the neglect of corrections due to 
the compression of the solution and of the solvent. Since then Prof. A. W. PORTER 
(' Proc. Roy. Soc.,' A, vol. 79, 1907) has put forward an exact equation in which the 
influence of these two factors can be taken into account ; increased experience with, 
and further modifications of, the vapour-pressure apparatus apparently justified the 
belief that the experiments would be more accurate, and therefore it seemed advisable 
to endeavour to obtain complete data for the aqueous solutions of some one substance, 
so as to test the practical applicability of the new formula in its entirety. 

The equation in question is 

rp r^oo rp PP 

sdp= Ydp+\ udp (1) 

Jw w > Jiroo 

and the notation is as follows : 

For the Solution : 

The hydrostatic pressure on the solution is p. 

The vapour pressure when the solution is in contact with its own vapour 

alone "V- 

Reduction of volume when 1 gramme of solvent escapes at pressure p . . s p . 

Osmotic equilibrium pressure for a hydrostatic pressure p Pp. 

VOL. CCIX. A 448. 2 A 28.11.08 



178 THE EARL OF BERKELEY, MR. E. G. J. HARTLEY AND DR. C. V. BURTON: 

For the Solvent : 

Specific volume at hydrostatic pressures p , TT W u pa . 

Vapour pressure when the solvent is in contact with its own vapour alone TT M . 
Specific volume of the vapour when under various pressures . . v, a , v, , &c. 

An examination of the equation will show that the following data are required : 

(1) The densities of solutions of different concentrations at the temperature at 

which the work was carried out, namely, C. 

(2) A series of measurements of the relative lowering of the vapour pressures of the 

solutions at C. 

(o) A corresponding series of measurements of the direct osmotic equilibrium 
pressures for the purpose of comparison with those to be deduced from the 
measurements of (2) by means of the equation. 

(4) Measurements of the compressibilities of the solutions and of water. 

(5) A knowledge of the change in the specific volume of water vapour with 

pressure this knowledge we assume is given by REGNAULT'S work. 

Choice of Solute. 

Owing to the fact that, in the direct measurement of osmotic pressures, the copper 
ferrocyanide membrane is semipermeable to but few substances, the choice is strictly 
limited. In calcium ferrocyanide a substance was found which seemed likely to throw 
considerable light on osmotic phenomena. 

Aqueous solutions of this substance have the following properties : The copper 
ferrocyanide membrane is practically impermeable to the salt. The salt is very 
soluble, so that strong solutions can be obtained and hence high equilibrium pressures ; 
the solutions at all strengths are apparently stable enough at C. to allow the 
necessary data to be obtained. The solutions show a considerable shrinkage on 
dilution, and this fact makes it possible to determine experimentally the s of the 
equation. 

In this part of the communication the work is limited to concentrations of from 
30 to 50 gr. anhydrous salt to 100 gr. of water. These limits are imposed 
upon us by the fact that weaker solutions have vapour pressures differing little 
from that of pure water, and, consequently, measurements of the relative lowering of 
their vapour pressures would entail very lengthy experiments,* while the stronger 
solution has an osmotic equilibrium pressure of about 130 atmospheres, which is near 
the utmost pressure we can obtain with our apparatus. 

* Even for a solution of 30 gr. anhydrous salt in 100 gr. water it is necessary to pass the air current 
through the vessels for a period of seven days before the difference between the loss of weight of the 
solution and that of the water is sufficient to give accurate results. 



OSMOTIC PRESSURES OF AQUEOUS SOLUTIONS OF CALCIUM FERROCYANIDE. 179 

General Scheme of Operations. 

About 500 c.cm. of solution are necessary for a determination of equilibrium 
pressure and vapour pressure ; as two independent measurements of these quantities 
are required at some five points in the total range of 40 to 130 atmospheres, it follows 
that a large amount of salt was necessary. 

To save salt, and in order to have a direct comparison between the two methods ot 
measuring osmotic pressures, it was decided to use the same " make up " of solution 
for both these measurements and the densities. The procedure adopted was to make 
up the solution in the morning (a portion of salt being set apart for analysis) and 
weigh it, and determine its density in the evening. The vapour-pressure vessels were 
then tilled and got ready for weighing ; and at the same time the direct osmotic- 
pressure apparatus was set up for "guard-ring leak" (see 'Phil. Trans.,' A, vol. 206, 
p. 490). The next morning the vapour-pressure vessels were weighed, placed in the 
bath, and the air current started ; meanwhile the direct determination of the 
equilibrium pressure was carried out and the tube set up for "solution leak" (Joe. cit., 
p. 493). 

Purification of the Salt. 

% 

The calcium ferrocyanide was obtained from Messrs. Kahlbaum as their purest. 
The first lot of about 2 kgr. was found to contain some potassium, probably in the 
form of the double salt. This lot, and also all succeeding ones, some 10 kgr. in all, 
was dissolved to foi"m as nearly a saturated solution at the laboratory temperature as 
possible (without warming), and then filtered through a Chamberland porcelain filter. 
The salt was then recovered by recrystallization. Various methods of recrystallization 
were tried, but the best was to pass, by means of a suction pump, a steady stream 
of filtered air over crystallizing dishes containing the solution, and at the same time 
maintain them at from 20-C. to 25 C.* The various crops were freed from mother 
liquor by means of a platinum ceutrifugalizing machine ; they were then powdered 
and dried in the air current at the temperature of the laboratory. 

Analyses of samples of the 1st and 2nd recrystallization showed no marked 
difference in composition, but it should be mentioned that sometimes the salt came 
out of solution slightly green instead of yellow, and although neither in analysis iior 
in the experiments (where want of the yellow salt compelled the use of the green) 
was there found to be any difference in the results, yet it was thought better to avoid 
the use of these crops as much as possible. It was found that, on prolonged standing, 
a trace of precipitate came out of solution this we suspected to be CaCO 3 , but tests 
failed to confirm this the quantity was not enough for analysis. 

The following table gives the analytical results : 

* The solutions seem to decompose at higher temperatures, 
2 A 2 



180 THE EARL OF BERKELEY, MR. E. G. J. HARTLEY AND DR. C. V. BURTON: 





1st lot. 


2nd lot. 


Percentage 
composition 
calculated 
from 
CaFe(CN) 6 llAq. 


1st 

recrystallization 
(yellow crystals). 


2nd 
recrystallization 
(yellow crystals). 


1st 
recrystallization 
(yellow crystals). 


1st 
recrystallization 
(green crystals). 


Fe(CN) 6 
Ca 
"Water 


per cent. 

43-41 
Not determined 
39-97 


per cent. 
43-24 
16-56 
39-92 


per cent. 

43-35 
16-63 
39-81 


per cent. 

43-27 
16-59 
39-93 


per cent. 
43-27 
16-34 
40-39 




99-72 


99-79 


99-79 


100-00 



It is to be noted that ROSCOE and SCHORLEMMER (2nd ed., ' Treatise on Chemistry, 
vol. ii., p. 1025), stated that the salt crystallizes with 12Aq; our results point, 
however, to llAq. 

The foregoing results, considering the imperfection of analytical methods, seemed to 
justify the assumption that the salt is of unvarying composition as far as the metallic 
radical is concerned ; hut as it is a highly hydrated salt, with presumably a vapour 
pressure, it was considered necessary to determine the water content of a sample 
of the salt used in each " make up " of solution. These determinations are given in 
the table of the results of the direct osmotic-pressure measurements (p. 191), and 
were obtained by drying the salt to constant weight in an air oven. 

DENSITIES. 

A 400 c.cm. and a 500 c.cm. flask were obtained, with graduated necks, whose 
diameter was such that 1 cm. of neck corresponded to 1 c.cm. capacity, and the 
graduations were in millimetres. The back of the neck was of milk glass, with a blue 
line running down the middle (Prof. SCHELLBACII'S device for burettes). By this 
means, readings estimated to O'Ol mm. could be obtained with fair accuracy. The 
necks were calibrated by adding weighed quantities of water to the flask (already 
filled with water) when in a constant temperature bath at C. and also at 30 C. 
The meniscus level was read through a telescope and care was taken to avoid parallax. 
The capacity of the flask was determined by weighing against a counterpoise on a 
large Oertling balance. 

A similar process was followed for the determination of the densities. The flask 
was filled, weighed, and placed in ice, and the level read when the solution had ceased 
contracting generally in about 5 hours' time. 

Experimental Error. 

It was found that the readings of the meniscus level could be relied on to 
0'01 mm.; this corresponds to a maximum error of 0'02 c.cm. on 400 c.cm., or 



OSMOTIC PRESSURES OF AQUEOUS SOLUTIONS OF CALCIUM FERROCYANIDE. 181 

1 part in 20,000. It was not considered necessary to correct for the volume of liquid 
above the bottom of the meniscus as the error appertains to both the determination of 
capacities and of the density. One uncertainty remains, in that when making up the 
solution, the neck above the level has been wetted and an unknown, arid possibly 
variable, quantity of liquid is left adhering. There is no means of correction for this, 
but the fact that the densities of slightly differing solutions generally follow the 
weight concentration indicates that this source of error is of no great importance. 

In the following table all the results on the densities of the solutions are given. 
The first column gives the weight concentration, i.e., the number of grammes of 
anhydrous salt in 100 gr. water, and the second gives the density. 

TABLE I. 



Weight concentration. 


Density at C. 


Weight concentration. 


Density at C. 


50-184 


1-32145* 


39-678 


1-26953 


49-913 


1-32168 


39-517 


1-26914 


49-875 


1-32138 


39-490 


1-26872 


49-827 


1-32086 


39-l'98 


1-26692 


47-292 


1-30912 


39-159 


1-26728 


47-146 


1-30808 


34-812 


1-24315 


44-167 


1-29314 


31'412 


1-22330 


44-114 


1-29341 


31-364 


1-22364 


42-900 


1-28660 


31-093 


1-22149 


42-878 


1-28662 







TABLE I A. Mean Values. 



Weight concentration. 


Density at 0" C. 


Weight concentration. 


Density at 0" C. 


49-872 
47-219 
44-140 


1-32131 
1-30860 
1-29327 


42-889 
39-408 
31-290 


1-28661 
1-26832 
1-22281 



LOWERING OF THE VAPOUR PRESSURE. 

During the progress of the research it was found that there was a disagreement of 
some two or three per cent, between the direct measurement of the equilibrium 
pressure and the same when calculated by means of PORTER'S equation from the 
lowering of the vapour pressure of the solutions. 

The cause of this discrepancy is surmised to be due to the fact that the experiments 
were carried out in air at atmospheric pressure, while Prof. PORTER'S equation implies 
vacuum conditions ; and although by modifying the equation to suit our requirements 
we obtain results (infra) which are in close agreement, yet the values for the vapour 

* This density was not used in the final computations it is known to be wrong sufficient time was not 
given for the temperature of the solution to become constant at C. 



182 THE EARL OF BEEKELEY, MR. E. G. J. HARTLEY AND DR. C. V. BURTON: 

pressure and density of water vapour in air, which are used in the reduction, may be 
somewhat in error.* It is, therefore, thought advisable to give somewhat full details 
of the various devices tried and of the test experiments made. 

Improvement in the Apparatus^ and Test Experiments. 

Method of keeping the Bath at C. A large wooden tub was kept filled with ice 
and water ; a small water pump, actuated by the laboratory shafting, pumped the 
water from the tub into the bath, and this water syphoned back into the tub. The 
temperature on a long run varied from about 0"2 to 1'0 C. It may be pointed out 
that the constancy of the temperature is not of so much importance as that there 
should be no difference between the temperatures of the various vessels in the bath. 
This was ensured by stirring the bath very vigorously and continuously. A ther- 
mometer placed in different positions in the bath showed no variation. 

Limits of Accuracy of Weighing the Glass Vessels themselves. 

One of the vessels was weighed four times, at intervals of a week or so, against the 
counterpoise, various operations having been performed on it between while, with the 
following results : 

Weight of vessel before experiment, 377925 gr. ; after, 377925, 377925, 
377923 gr. 

Another vessel, fitted with mercury cups (see infra, fig. 3, p. 186), was similarly 
weighed. The cups, after mercury had been poured into and out of them, were 
cleaned witli nitric acid, dried with alcohol, &c. : 

Weight of vessel before experiment, 29 '2700 gr. ; after various washings and 
leaving in the bath for a week, 29'2760, 29'2759, 29'2759, 29'2758, 29'2760, 
29-2756, 29-2755 gr. 

The change shown in the last two experiments is probably due to the balance 
wanting cleaning. From these numbers it will be seen that the maximum error is 
only G'0005 gr. 

New Form of Joint between Water and Sulphuric Acid Vessels. 

The method adopted for measuring the relative lowering of the vapour pressure of 
the solution is that described in the ' Roy. Soc. Proc.' (BEKKELEY and HARTLEY, 
vol. 77, A, 1906). The solution is contained in two vessels which are weighed 
separately. Dried air passes over the solution in these vessels in series; it then passes 
over water in a weighed vessel, and finally over sulphuric acid in a fourth weighed 
vessel. The assumption on which the method is based is that the air, on emerging 

* The values are derived from REUNAULT'S work, but he himself seems somewhat dissatisfied with them, 
t Described 'Roy. Soc. Proc.,' vol. 77, A, 1906, pp. 156, 162. 



OSMOTIC PRESSURES OP AQUEOUS SOLUTIONS OF CALCIUM FERROCYANIDE. 183 

from the 2nd solution vessel, is saturated with water vapour up to the vapour 
pressure of the solution, and on emerging from the water vessel it is then saturated 
up to the vapour pressure of the water. Hence the ratio of the loss of weight of the 
vessels containing the solution to the sum of the loss of weights of solution and water 
vessel equals the ratio of the density of the vapour over the solution to that over 
water. As pointed out in the communication mentioned above, it is evident that if 
the air on entering the train of vessels has been dried by sulphuric acid, and on 
emerging from the water vessel it is again dried in a similar manner, the gain in 
weight of the 4th vessel (the vessel containing the sulphuric acid) should equal the 
sum of the losses of weight of the solution and water vessels. In that paper it was 
shown that this did not obtain -there was a considerably greater loss of weight than 
there was gain by the 4th vessel. This discrepancy can be shown to be partly caused 
by the saturated air giving up some of its moisture* to the tube connecting the 3rd 
and 4th vessels. 

As it was found to be impossible to weigh accurately the connecting tube, it was 
sought to bring the deposited moisture into the sulphuric acid by making the internal 
diameter of this tube only 1/5 mm., so that the velocity of the air current would 
sweep the moisture forward. 

Fig. 1 (p. 184) shows the first form tried and is self-explanatory. 

The use of the joint in this form, and other modifications of it which need not be 
further described, caused a considerable improvement, as shown by the following test 
experiments : 

Air was passed very rapidly for 24 hours through two vessels in series, joined by 
the above-mentioned form of joint. The 1st vessel contained water and the 2nd 
sulphuric acid. The temperature of the bath was constant at about 30 0. 

The water lost 2'8425 gr. 

The sulphuric acid gained 2'8393 gr. 

The "dipping" tube (i.e., the tube connecting the water and sulphuric acid vessels) 
was found to have gained 0'0048 gr. 

The difference between the losses and gains being, therefore, +0 - 0016 gr. 

A repetition of the experiment with a slow air current gave a difference of 
-0-0003 gr. 

* There are three plausible explanations of the phenomenon : (1) That there are eddy currents (possibly 
caused by inequalities of surface) in the junction tube and the consequent changes of temperature bring 
about deposition ; in this connection it is noteworthy that more moisture is deposited on a dirty tube. 
(2) That the surface of any glass vessel is always slightly hydrated, and if the glass be soluble a solution 
of lower vapour pressure is formed, and, consequently, more moisture is deposited ; evidence in favour of 
this view is afforded by the well-known fact that less moisture is deposited on lead glass, which is stated to 
be less soluble than soda glass ; on the other hand, we find that we get the usual deposit on platinum- 
iridium tubes. (3) That the air, containing ions, is really supersaturated in as far as the ions may carry a 
watery envelope ; the latter is deposited on the walls of the tube where the ions come in contact with it. 
We are at present engaged in experiments to test this hypothesis. 



184 THE EARL OF BERKELEY, MR. E. G. J. HARTLEY AND DR. C. V. BURTON: 



Rubber 
Cubing 




Rubber 
tubing 



Exit tube of 
waCer vessel 



Rubber plug 



Fig. 1. 

Change in Weight of 2nd Solution Vessel. 

It was mentioned that the 2nd solution vessel always lost weight (see p. 163 of 
vol. 77, A, 'Roy. Soc. Proc.'), and a possible explanation was suggested for this. Further 
work with the method seemed to point to the absorption of moisture by the rubber 
connecting piece as a possible cause of the difficulty. Fig. 2 (p. 185) shows the form of 
joint devised to get over this. A is the exit tube of one vessel, and B the entry tube 
of the next vessel. C is a rubber plug, cut on the lathe to the shape shown, and 
secured in place by the "umbrella rings" D. The inverted U-tube E is similarly 
held in place by F, and the space between the U-tube and the exit and entry tubes 
A and B is partially filled with- mercury through the side tubes G, which are themselves 
closed by rubber plugs. 

The following tests were made : 

Two vessels, containing sulphuric acid, were placed in series and dry air passed for 
48 hours, with the result that each vessel gained 0'0006 gr. 

This experiment was repeated and air passed for 116 hours, at the end of which 
the 1st vessel had gained 0'0022 gr., and the second 0'0032 gr. 

The experiment was again repeated, but the precaution was taken to dry the 
rubber plugs in an air oven and keep them in a desiccator until use, as it might be 
that these plugs gave up moisture to the mercury which passed it on to the air 



OSMOTIC PRESSURES OF AQUEOUS SOLUTIONS OF CALCIUM FERROCYANIDE. 185 

current. A run of 70 hours resulted in a gain of weight in the 1st vessel of 
O'OOOS gr. The weight of the 2nd vessel was lost by an accident. 

This experiment was again repeated with three vessels in series, the only change 
being the use of graphite as a lubricant for the rubber plugs. A run of 70 hours gave 
a gain in 1st vessel = 0'0045 gr., in 2nd 0'0034 gr., in 3rd O'OOIO gr. 



G- 




Fig. 2. 






Another run of 70 hours resulted in a gain of 0'0032 gr., O'OOl 9 gr., and O'OOOO gr., 
respectively. 

The rubber plugs were then given \ip and a plain mercury cup joint used, as in 
fig. 3 (p. 18G). 

A and B are the exit and entry tubes of the vessels, C C are the glass cups, fused to 
A and B, to contain the mercury. The inverted U-tube D is held in position by a 
clamp (not shown) supported from the oscillating platform. 

The following tests of this joint were made : 

Three vessels, containing sulphuric acid, were placed in series, and air passed for 
92 hours; 1st vessel gained 0'0035 gr., 2nd O'OOOS, and 3rd 0'0025 gr. 

It was thought that possibly the cups were not properly cleaned out before 
weighing, as it was found that the water of the bath had, during the experiment, 
become charged with rust from the clamps. A repetition of the experiment on a 
116-hour run (using brass clamps) gave gains of - 0045 gr., 0'0021 gr., and O'OOIG gr. 
respectively. In both these experiments the temperature of the bath was that of 
the laboratory. 



VOL. CCIX. A. 



2 B 



186 THE EARL OF BERKELEY, MR. E. G. J. HARTLEY AND DR. C. V. BURTON: 



c 



c 




Fig. 3. 

Pure Air. 

It was now noticed that although the air passing through the train of vessels was 
filtered, yet a certain amount of reaction had taken place in the 1st sulphuric acid 
vessel (vessel D of original paper), for the acid had turned brown during the course 
of the experiments. This was completely remedied by drawing the air from outside 
the laboratory and by avoiding rubber tubing on the entry side. This latter 
modification was obtained by means of a mercury cup placed outside the bath, but in 
the axis of oscillation of the platform. 

An experiment with four sulphuric acid vessels in series was then made, with the 
air current running for 92 hours, the temperature of the bath being constant at about 
30 C. The 1st vessel gained 0'0021 gr., 2nd O'OOIO gr., 3rd 0'0012 gr., and 4th 
O'OOIS gr. It was now thought that possibly these changes in weight were due to the 
absorption of mercury vapour by the sulphuric acid. An attempt to test this was 
made by furnishing two out of the four vessels with gold sleeves suspended in the 
entry tubes. A run of 92 hours at 30 C. gave O'OOIS gr., 0'0013 gr., 0'0004 gr., and 
O'OOIO gr. respectively, and the gold sleeves were not found to have altered in weight. 

Hitherto the vessels, while on the balance, had not been closed ; in view of the fact 
that the errors now seemed to be considerably less than heretofore, it was thought 
better to have vessels made with their entry and exit tubes fitted with ground- 
glass stoppers. These vessels were then tested as before. 



OSMOTIC PRESSURES OF AQUEOUS SOLUTIONS OF CALCIUM FERROCYANIDE. 187 



Run. gr. 

hours at 30 C. gave +0'0004 
30 +0-0005 
90f 30 +0-0005 
115 +0-0003 



gr- 
+ 0-0011 

+ 0-0007 
+ 0-0010 

+0-0001 



+ 0-0006 
+ 0-0008 
+ 0-0013 
+ 0-0008 



and 





Average. 


P- 


g r - 


+ 0-0001, 


0-OOOG. 


+ 0-0007, 


0-0007. 


+ 0-0007, 


0-0009. 


o-oooo, 


0-0003. 




It will be noticed that the gains are greater for the higher temperatures than for 
the lower, and, further, the average gain shows a tendency to increase with increased 
length of run. Both facts are explicable on the assumption that the gains are due 
to mercury vapour, and it is noteworthy that, calculating from the approximately 
known vapour pressure of mercury (LANDOLT and 
BORNSTEIN'S tables) and estimating the amount of 
air passed (from previous work), the gains are 
found to be of the order of the number given from 
these data. Exact concordance cannot be expected, 
because in all experiments the inverted U -tubes 
(fig. 3, p. 186) were brought down as close to the 
exit and entry tubes as was practicable. 

It was therefore decided to test this question 
by using a form of joint which avoided the use of 
mercury. For this purpose Messrs. Johnson and 
Matthey made inverted U -tubes of platinum- 
iridium (see fig. 4) in such a way that they were 
not rigid and, consequently, allowed the unavoid- 
able expansion and contraction, when the whole 
train of vessels was put into and taken out of the 
bath, to take place without risk of breaking the 
glass vessels or unduly straining the joints. 

A and B are the exit and inlet tubes, and the 
inverted platinum-iridium U-tube C is ground into 
these at D and E. The internally conical parts E 
and F are for the ground-glass stoppers (not shown) 
used when weighing the vessels. The upper part 
of the U-tube is of thin tubing and is flexible. 
This joint was tested, after some preliminary 
experiments, as follows : 






E- 



C 



D- 



-B 





Fig. 4. 



Two sulphuric acid vessels in series were joined by one platinum-iridium joint and 
air passed for 63 hours at 30 C. (rubber lubricant in ground joint). There was a gain 
in the 2nd vessel of 0'0004 gr. Another run of 72 hours at 30 C. gave a gain 
of O'OOOl gr. Three vessels in series, run of 116 hours at 30 C., with a dry-air 
current, gave losses O'OOOl gr., O'OOOl gr., 0'0004 gr. 

2 B 2 



188 THE EAKL OF BERKELEY, ME. E. G. J. HARTLEY AND DR. C. V. BURTON: 

This seems to show conclusively that some of the previous gains in weight were due 
to mercury vapour. 

As the gain at C. (see p. 187) was only 0'0003 gr. for 116 hours' run, it was 
decided to use this form of vessel (i.e., mercury cups) for work at C., and to reserve 
the platinum-iridium U -tubes for work at 30 C. 

Test of Fall of Air Pressure. 

In connection with the change of weight in the 2nd solution vessel it was thought 
possible that the loss might be due to a difference of pressure in the air current, caused 
by " wire-drawing " the air when passing over and through the platinum rolls. 

The total difference in the pressure of the air when entering and when leaving the 
train of vessels at a rate of 50 bubbles in 11 seconds was determined and was found to 
be about 1 mm. of water. This number, even if the whole difference of pressure were 
supposed to take place between the two solution vessels, is inadequate to account for 
the loss of weight observed. 

Text to tee whether the Oscillation of the Vessels causes any Change. 

It was thought that the oscillation of the train of vessels might affect the results; 
for J. J. THOMSON and others have pointed out that the surface layer of a solution is 
at a different concentration to that of the bulk of the liquid. Now, in the method of 
operation adopted, the air is caused to pass over platinum rolls recently wetted by 
the solution, and from which the solution is slowly draining off. It might be that a 
layer of solution thus left in contact with the air has a different concentration to that 
of the ordinary surface,* arid this effect was looked for by setting up a vapour-pressure 
experiment without oscillating the apparatus nor using the platinum rolls, but passing 
the air over at a slower rate. No appreciable difference resulted (see experiment 
marked * on next page). 

In the following table all vapour-pressure results with Ca 2 Fe(CN) 6 solutions are 
given. 

The 1st column gives the date of the beginning of the experiment; the 2nd gives 
the weight concentration of the solution used, i.e., the number of grammes of 
anhydrous salt to 100 grammes of water, and is calculated from the analyses given in 
the table on p. 191, column 3 ; the 3rd gives the mean temperature of the bath ; the 
4th gives the number of hours the air was passing ; the 5th gives the rate of bubbling, 
i.e., the time taken for 50 bubbles to pass ; the 6th, 7th, 8th and 9th give the changes 
in weight in the several vessels. It is to be noted that the algebraic sum of the 

* Another disturbing factor is that the small radius of curvature of the surface of the solution clinging 
to the thin edges of the platinum rolls raises the vapour pressure ; the experiment without the platinum 
rolls shows that the joint influence of this together with that indicated in the text is of no practical 
importance. 



OSMOTIC PRESSURES OF AQUEOUS SOLUTIONS OF CALCIUM FERROCYANIDE. 189 





c-i 

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8 


55?^^^55ss^ 


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1-H 


1 


1|i|lH11|111 

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S I'e 

1 &- 

^ o - 

1 gt 

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K* 2 S 

w o | 

* *- JJ 

o 
C 



190 THE EAKL OF BERKELEY, MR. E. G. J. HARTLEY AND DR. C. V. BURTON: 

TABLE HA. Mean Values. 



Weight 
concentration. 


klh- 


49-966 


1-10710 


47-219 


1-09167 


42-889 


1-07017 


39-503 


1-05708 


31-388 


1-03316 



numbers in the horizontal row included in columns 6 and 7 gives li ; the 1 Oth gives 
the total loss of weight of solution and water, = 1 ; the llth gives the total gain, 
including the amount of moisture found in the "dipping tube," while the 12th gives 
the ratio of the vapour pressure of water to that of the solution and is obtained by 
dividing the total loss by the loss of weight of the solution, = ?//!. 

Remarks on the Table. 

It will be noticed that the ratios of 1 to l for experiments with similar concen- 
trations are in very close agreement. 

It should be mentioned that at first, in these experiments at C., a difficulty was 
experienced in that the sulphuric acid in the first branch of the last vessel crystallized 
out during the run. Now, the freezing-point of the hydrate H 2 SO 4 lAq is higher 
than C., hence when the pure acid in the first branch takes up enough water 
to form a liquid of that concentration it solidifies, but the addition of more water will 
lower the freezing-point. The difficulty, therefore, was overcome by filling this first 
branch, at the start, with an 85-per cent, solution of sulphuric acid, i.e., a solution 
slightly weaker than H 2 S0 4 lAq. 

OSMOTIC EQUILIBRIUM PRESSURES. 

The equilibrium pressures were determined in exactly the same way as described in 
'Phil. Trans.,' A, vol. 206, pp. 481-507. 

It is only necessary, before giving a table of the results, to call attention to the fact 
that in all cases the " solution-leak correction," that is, the amount of calcium ferro- 
cyanide which came through the membrane during the experiment, is practically 
negligible. The amount coming through was determined by evaporating the water 
contents of the tubes together with 100 c.c. washing water passed through the tube 
after an interval of four days, down to a small bulk, and determining the calcium in 
it by the oxalate method. 

It should be mentioned that the solutions act on the gunmetal of the osmotic 
apparatus ; this was prevented by coating the metal with a varnish. 

In Table III., Column (l) gives the date of the experiment; (2) the weight 
concentration (i.e., the number of grammes of anhydrous salt to 100 grammes of 



OSMOTIC PRESSURES OF AQUEOUS SOLUTIONS OF CALCIUM FERROCYANIDE. 191 



a 


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H 



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1 



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3 



192 THE EAKL OF BERKELEY, MR. E. G. J. HARTLEY AND DR. C. V. BURTON: 

TABLE IIlA. Mean Values. 



Weight 


Osmotic equilibrium 


concentration. 


pressure. 




atmospheres 


50-048 


131-21 


47-219 


112-84 


42-889 


87-09 


39-503 


70-84 


31-388 


41-22 



water) of the solution ; (3) the water content of the hydrated salt used in the " make 
up " of the solution ; (4) the name of the tube used ; (5) the apparent turning-point, 
i.e., the pressure at which no movement of the water gauge takes place; (6) the 
movement of the water level, in millimetres, in 15 minutes, caused by the "guard-ring 
leak" ; (7) the time the pressure was on the solution ; (8) the solution leak, i.e., the 
total amount of Ca a Fe(CN) come through the membrane during the time in 
Column (7) ; (9) the movement of the water level, in millimetres, in 15 minutes, 
caused by an increment of pressure of "3 4 atmosphere ; (10) the apparent turning- 
point [Column (5)], corrected for "guard-ring leak"; as there is practically no 
correction for "solution leak," the numbers in column (10) can be taken as the osmotic 
equilibrium pressure of the solution when there is a pressure of 1 atmosphere on the 
solvent. 

COMPRESSIBILITY OF THE SOLUTIONS. 

An attempt was made, in view of other work with more compressible solutions, to 
design the apparatus so that accurate results might be obtained. The piezometer is 
represented by fig. 5. The gunmetal vessel A is filled with water and connected by 
B and C to a Schaffer and Budenberg dead-weight pressure apparatus. 

The " llobax " * Jena glass tube D, 19 mm. external and 12 mm. internal diameter, 
is made pressure-tight with the gunmetal piece E by means of a dermatine ring F, 
which is compressed between a shoulder and a metal sleeve actuated by a nut, J. 
The lower end of the tube is closed pressure-tight in a similar manner and the tube is 
prevented from slipping out by four distance stays such as G G. The compressibility 
vessel H, which is filled with the solution to be examined, is of No. 16 m Jena glass. 
This glass was selected as its compressibility has been carefully determined by SCHOTT 
and STRAUBEL.f The bulb is of about 15 c.cm. capacity and the stem, open at the 
lower end, is graduated into millimetres (1 mm. of the bore has a -capacity of 
0'0002 c.cm.). The whole tube, bulb, and stem were carefully calibrated in the usual 

* The Robax tubes were found to withstand pressure fairly well, but after considerable use they burst 
at a lower pressure than that originally reached ; hence, after using a tube for four or five observations at 
100 atmospheres, it must be replaced by a new one. 

t SCHOTT and STRAUBEL see references in LANDOLT and BORNSTEIN'S tables, 3rd ed. 



OSMOTIC PKESSURES OF AQUEOUS SOLUTIONS OF CALCIUM FERROCYANIDE. 193 

way by means of mercury. The stem was made 40 cm. long, and its bore such that 
an appreciable change in reading could be observed even when caused by only a 
change of pressure of a few atmospheres. 

The bottom of the Robax tube is filled for some few centimetres with mercury and 
matters are so arranged that the mercury rises in the stem of the compressibility 
tube H a centimetre or two above the level of the mercury outside when the whole 
apparatus has been brought to a constant temperature at atmospheric pressure. 





Fig. 5. 



Fig. 6. 



General Method of Experiment. 

The compressibility tube is filled as shown in fig. G, which represents the method 
adopted to fill with air-free liquid. The compressibility tube A is joined at its lower 
end to a bulb, B, containing the liquid, and at its upper end to the U-tube C 
containing pumice moistened with sulphuric acid; this U-tube is weighed before and 
after the experiment. The U-tube is connected at D to a Fleuss exhaust pump by 
flexible pressure tubing ; the T-piece E serves to connect it to the other end of the 
bulb containing the solution through the three-way tap F. By closing tap G, 
turning F so as to have through communication, and opening tap H, the liquid in B 
can be caused to boil. Care, however, must be taken only to create a vacuum 
above B sufficient to get rid of the air (shown by air bubbles coming off), otherwise 
an unnecessary increase of concentration of the solution in B will take place. When 

VOL. ccix. A. 2 c 



194 THE EARL OF BERKELEY, MR. E. G. J. HARTLEY AND DR. C. V. BURTON: 

it is judged that practically all dissolved air has been removed, tap H is closed 
and G opened ; the aim is to sweep out any air adhering to the sides of A by a 
current of moisture. Tap G is then closed, and the whole apparatus tilted to the left, 
so that the liquid in B closes the left-hand orifice ; the tap H is then opened and F is 
cautiously turned so as to admit air above the solution. In this manner the 
compressibility tube is filled up to the tap without any air bubbles being apparent, as 
a rule. The key of tap G must also be filled, otherwise deformation may take place 
when the vessel is placed under compression. The compressibility tube is then taken 
down and placed in the piezometer. 

Now, if the bulb B has been filled with a known volume of solution whose density 
and concentration are known, and the change in weight in C is known, then the 
concentration of the solution tilling the compressibility tube is known. 

All the experiments on compressibility here given were those obtained at C. 
For this temperature, after the introduction of the compressibility tube, the whole 
apparatus was filled with ice-cold water and the upper part, down to 3 or 4 cm. 
below the coupling J of fig. 5, was surrounded by ice. A period of some four or five 
hours, the ice being rammed down at intervals, was allowed to elapse so that a 
constant temperature approximating to C. might be attained. The constancy of 
the temperature was judged by readings of the mercury level in the compressibility 
tube,* the readings being taken by means of a telescope. 

A pressure of some 20 atmospheres was then gradually put on the water in the 
apparatus and when the level of the mercury in the compressibility tube was constant 
it was noted. Another gradual increase of pressure of the same amount was then 
put on and the level read, and so on till the maximum pressure of about 100 
atmospheres was attained, after which the reverse process was carried out. 

The intention had been to reach a pressure of 150 atmospheres, but, although at 
times the " liobax " tubing stood this, one or two serious breakages (causing in one 
case the fracture of the compressibility tube) made it desirable to limit the experiment 
to 100 atmospheres. 

Sources of Error. - 

There seem to be two main sources of error : 

(l) Variation of temperature during the experiment. There are two causes for a 
change of temperature. One is that the ice in melting round the apparatus causes a 
small quantity of warm air to come into contact with the gunmetal casting. This 
was obviated by ramming the ice down at intervals of about 15 minutes. The 
second cause of a change of temperature is unavoidable and is due to the development 
of heat by the compression of the liquid itself. This thermodynamic change of 
temperature was found to disappear in about 10 minutes. 

* In later work the piezometer was altered so that a mercury thermometer could be placed close to the 
compressibility tube. 



OSMOTIC PRESSURES OF AQUEOUS SOLUTIONS OF CALCIUM FERROCYANIDE. 195 



(2) A possible source of error is the presence of lubricant in the tap at the top of 
the compressibility tube and also any unobserved air bubbles in the solution. 

It was considered that these errors were overcome when the same reading of the 
mercury level in the compressibility tube was obtained for the same pressure reading, 
whether when increasing the pressure or when decreasing it. On the other hand, it 
was noticed that on increasing the pressure somewhat quickly the rapid rise of the 
mercury in the stem of the compressibility tube caused it to enclose small globules of 
liquid which further inci'ease of pressure did not seem to move, hence the apparent 
constancy of the change in volume for a given change in pressure may be no 
indication that the true change in volume has been obtained. 

It was found, however, that the enclosed globules of liquid were avoided when the 
rate of change of pressure was slow. 

The following is from the laboratory book and gives the details of one of the 
experiments with calcium ferrocyanide solution. 

The solution was made up by weight in the 400 c.c. flask and its density 
determined as on p. 180. 



Date. 



March 18 
March 19 



Weight of 
U-tube. 

70-584gr. 



Time. 



9.0 A.M. 
10.45 
11.5 
11.15 
11.35 



12. 40 P.M. 70-612 gr. 



Remarks. 



Made up solution. 

Used No. II. compressibility tube. 

Filled bulb and connected up as before (i.e., as in fig. G). 

Started pumping. 

Opened bulb to pump for 5 seconds. 



Closed taps and opened compressibility tube to pump. 
Closed compressibility tube and filled. 

Withdrew compressibility tube and placed its bulb in ice for 
2 minutes while lower end dipped in solution and then 
placed in apparatus which was immediately filled with ice- 
cold water and covered with ice. 



During the afternoon the ice was rammed down at intervals of one hour, and at intervals of a quarter 
of an hour between 4 and 5 P.M. 



Date. 



March 19 





Pressure 


Reading 


Difference 


Time. 


in 


of 


of 




atmospheres. 


stem. 


pressure. 


P.M. 




mm. 




5.5 


1 


63-3 




5.9 


21-4 


102-2 




5.14 


21-4 


102-8 




5.19 


21-4 


102-85 


20-412 


5.22 


41-8 


140-4 




5.27 


41-8 


141-1 




5.32 


41-8 


141-15 


20-412 


5.34 


62-2 


177-9 




5.39 


62-2 


179-0 




5.45 


62-2 


179-05 


20-412 



Difference 

of Remarks, 

reading. 



32-55 



38-3 



37-9 



Rammed down ice. 



Rammed down ice. 



Rammed down ice. 



2 C 2 



196 THE EAEL OF BERKELEY, MR. E. G. J. HARTLEY AND DR. C. V. BURTON: 



Date. 



March 19 





Pressure 


Reading 


Difference 


Difference 


Time. 


in 


of 


of 


of 




atmospheres. 


stem. 


pressure. 


reading. 


P.M. 




mm. 




mm. 


5.46 


82-6 


215-0 






5.51 


82-6 


215-7 






5.56 


82-6 


215-8 


20-412 


36-75 


5.59 


103-1 


251-0 






6.4 


103-1 


252-0 






6.9 


103-1 


252-0 


20-412 


36-2 


6.10 


82-6 


216-6 






6.15 


82-6 


216-0 






6.20 


82-6 


215-95 


20-412 


36-05 


6.22 


62-2 


180-1 






6.27 


62-2 


179-2 






6.32 


62-2 


179-1 


20-412 


36 85 


6.33 


41-8 


142-0 






6.38 


41-8 


141-2 






6.43 


41-8 


141-15 


20-412 


37-95 


6.44 


21-4 


103-4 






6.49 


21-4 


102-7 






6.54 


21-4 


102-7 


20-412 


38-45 


6.58 


1 


64-4 






7.3 


1 


64-1 






7.8 


1 


64-05 


20-412 


38-65 



Remarks. 



Rammed down ice. 



Rammed down ice. 
Rammed down ice. 
Rammed down ice. 
Rammed down ice. 
Rammed down ice. 



The weight concentration of the solution before filling the compressibility tube was 38-812 gr. of 
anhydrous salt to 100 gr. of Aq and its density 1 2432 at C. 50 c.cm. of this solution were pipetted into 
the bulb and, during filling, gave up to the H 2 SO 4 U-tubc a weight of 0-028 gr. of water, from which it is 
deduced that the concentration of the solution filling the compressibility tube was 38-834 gr. 



Reduction of Observations of Compressibilities. 

(1) Determination of Compression of Compressibility Tube. The observed change 
in volume of the liquid filling the compressibility tube is the algebraic sum of two 
terms the actual change of the liquid less that due to the glass itself. 

As stated, the compressibility tube was made of Jena glass 16 111 and the compressi- 
bility of this glass has been worked out by STRAUBEL* and others (see LANDOLT and 
BORNSTEIN'S tables, 3rded., for references) to be '00000228 per atmosphere at ordinary 
laboratory temperature. 

There seems to be good reason for believing that AMAGAT'S value for the compression 
of mercury is accurate (see JAMIN, ' Cours de Physique '), so that by using this value 
and observing the apparent change in volume of the compressibility tube when rilled 
with mercury a check on the above coefficient of the glass can be obtained. 

An experiment in which the compressibility tube was exhausted by means of a 
Gaede pump and then filled by recently redistilled mercury gave 4 0169 as its 
apparent coefficient of compression in the compressibility tube between 1 and 101 

* The value in LANDOLT and BORNSTEIN'S tables seems to have been derived from torsion and bending 
experiments. 



OSMOTIC PRESSURES OF AQUEOUS SOLUTIONS OF CALCIUM FERROCYANIDE. 197 

atmospheres at C. AMAGAT'S value for the true coefficient is 0'0 4 0392 ; hence that 
of the glass is 0'0 4 0223 at C. 

The agreement between this result and STRAUBEL'S value seems to prove that no 
serious experimental error has been incurred. 

(2) Corrections to be Applied to the Volume Reading. The method used is based 
on the assumption that the pressure inside and outside the compressibility tube is the 
same, but it must be remembered that this can only be the, case at the be<riiminir 

/ O O 

of the experiment (i.e., when the level of the mercury is the same inside and outside 
of the compressibility tube), for when the mercury has been caused to rise in the stem, 
there is an excess of pressure on the outside of the compressibility tube due to the 
amount of the rise of the mercury above the level outside. The change in volume of 
the compressibility tube due to this was determined by special experiments, and a 
correction has been applied to both the volume and the pressure. The latter 
correction, in view of the nature of the results required in this paper, is of no 
importance. 

Results. 

The following tables give the corrected results obtained : 



EXPERIMENTS on the Compressibility of Water at C. 

The 1st column gives the range of pressure in atmospheres ; the 2nd column gives 
the coefficient of compression per atmosphere in that range ; the 3rd column gives 



AMAGAT'S results for the same range. 



Pressure range, in 
atmospheres. 


Observed coefficient 
of compression. 


AMAGAT'S coefficient. 


Remarks. 


1-0 to 62-2 
13-6 74-8 
1-0 62-2 


0-00005117 
0-00005114 
0-00005132 


0-0000518 
0-0000515 
0-0000518 


Air-free water (f hour "boiling"). 

n j) \ / 

Water not quite free of air. 



The compressibility of the calcium ferrocyanide solution is only required for the 
purpose of calculating the osmotic equilibrium pressure from vapour-pressure measure- 
ments, and as the latter were only made on solutions whose weight concentration 
varied from 50 to 31 gr. of anhydrous salt per 100 gr. of Aq, the compressibility 
measurements recorded here were restricted to this range. 

The following table gives the results obtained for the solutions at C. Column 1 
gives the weight concentration in grammes of anhydrous salt per 100 grammes of 
water of the solution ; column 2 gives the range of pressure ; column 3 gives the 
corresponding coefficient per atmosphere : 



198 THE EARL OF BERKELEY, MR. E. G. J. HARTLEY AND DR. C. V. BURTON: 



Concentration 


Pressure range, in 


Coefficient per 


Concentration 


Pressure range, in 


Coefficient per 


before filling. 




atmospheres. 


atmosphere. 


before filling. 


atmospheres. 


atmosphere. 




r 


1-0 to 14-6 


0-0 4 265 


f 


1-0 to 21-4 


0-0 4 238 






14-6 28-2 


4 262 




21-4 48-6 


4 234 


^!Q -7 




28-2 41-7 


4 260 


47-3 


48-6 75-8 


4 234 


oy i 




41-7 55-3 4 253 




75-8 103-1 


4 232 






55-3 68-9 4 259 


I 


103-1 116-7 


4 229 






68-9 82-5 


4 255 









These two experiments were of the nature of preliminary experiments ; the data 
for calculating the density of the solution filling the compressibility tube were not 
obtained, nor was great care taken to avoid concentrating the solutions while 

" boiling " off the dissolved air. 

TABLE IV. 



1 










Weight 


Pressure range, in 


Coefficient per 


Weight 


Pressure range, in 


Coefficient per 


concentration. 


atmospheres. atmosphere. 


concentration. 


atmospheres. 


atmosphere. 


50 9* 


1 to 140 0-0 4 235 


r 


1-0 to 21-4 


0-0 4 287 








21-4 41-8 


4 280 






34-83 \ 


41-8 62-1 


4 280 


r 


1-0 to 21-4 4 233 




62-1 82-4 


4 278 




21'4 41-8 , 0,225 


[ 


82-4 102-8 


4 276 


49 95 


41-8 ., 62-1 , 4 229 










62-1 82-4 4 227 






I 


82-4 102-8 4 220 


Mean coefficient = 


4 280 


Mean coefficient = 


4 227 


r 


1-0 to 21-4 


4 305 








21-4 41-8 


4 295 






3l-09f <( 


41-8 62-1 


4 299 


r 


1-0 to 41-8 4 251 




62-1 82-4 


4 296 


44-21 J. 


41-8 62-1 


4 245 


I 


82-4 102-8 


4 290 


} 


62-1 82-4 0..245 






( 


82-4 ., 102-8 i 4 245 










Mean coefficient *= 


4 297 


Mean coefficient = 


4 247 








f 


1-0 to 21-4 


4 255 




1 


21-4 41-8 


4 263 




39-28 


41-8 62-1 


4 264 






62-1 82-4 


4 260 




I 


82-4 102-8 


4 268 




Mean coefficient = 


4 262 





^ This experiment was not finished owing to breakage. 

t This experiment was made on a solution which was not freed from air at all, and, on plotting the 
several results, it appears to come on the curve, from which it would seem that dissolved air has no 
appreciable influence on the coefficient. 



OSMOTIC PRESSURES OF AQUEOUS SOLUTIONS OP CALCIUM FERROCYANIDE. 199 

MODIFICATION OF PORTER'S EQUATION. 

The experiments on vapour pressures and on the equilibrium pressure were done in 
air, but Prof. PORTER'S equation is derived from the consideration of somewhat ideal 
conditions approximating to that of a vacuum, and it is therefore necessary to obtain 
an expression suitable to the conditions of the actual experiments. 

This may be derived in the following manner : 

Assume that the pistons in the ideal apparatus are permeable to air but not to the 
liquids or their vapour, then no work can be done on or by the atmosphere. 

Using the notation on p. 177 with the additional symbols 

A = pressure of the atmosphere ; 

7r n0 = vapour pressure of the solvent in air when it is under a total pressure 
of A + 7r au ; 

Tr a , = vapour pressure of the solution in air when it is under a total pressure 
of 



and performing the thermo-dynamic cycle, as in Prof. PORTER'S paper, it is easily seen 
that the work done in the various operations is : 



1st operation. P<A +*)%+, ~ (/V 

f"(A + ir ) 

2nd operation. pdnir M v n +(A + 7r,, (l ) ?/ (v+ff >. 

3rd operation. "" p dv. 

pA + n- f"A+7T 

4th operation. pdV-+ir a ,v a , (A.+ir t , r )8 (fL +, } + \ *pd(V+s). 
Summing up, equating to zero, and integrating by parts, we get* 

sdp = \" vdp+\ udp (2). 

jA+ ' r ,, n . J W JA+ *O 

This equation is, in appearance, the same as Prof. PORTER'S, with the limits slightly 
altered ; yet if we carefully consider what assumptions underlie the various operations, 
it will appear that the quantities involved are different. 

* Since this was written, Prof. PORTER has published the second part of his paper " On the Osmotic 
Pressure of Compressible Solutions of any Degree of Concentration" ('Proc. Roy. Soc.,' A, vol. 80) ; he points 
out, in a private communication, that equation (2) may be directly obtained, as in Section 5 of that paper, 
by estimating (throughout the cycle) the changes in jt> dp, which must vanish also because this integral is 
the same as \pv\ - \pdv. 



200 THE EARL OF BERKELEY, MR. E. G. J. HARTLEY AND DR. C. V. BURTON: 

We have tacitly assumed that the actual semi-permeable membrane is impermeable 
to the air dissolved in both solution and solvent ; so that the s of the equation is the 
actual change in volume under the conditions of the experiment. This element will 
be given by the density measurements in conjunction with the measurements of 
the compressibility of the solutions and of water, which in all cases contain 
dissolved air. 

The u term is similarly obtained ; although this term, as will be seen later on, is of 
no importance in this work, it may be so when dealing with liquids that are more 
volatile than water ; then the compressibility of air-containing solvents will have 
to be obtained with considerable accuracy. It should be noted that the P of the 
limit represents the actual osmotic equilibrium pressure due both to the dissolved salt 
and the dissolved air in the solution measured against the back osmotic pressure of 
the air dissolved in the otherwise pure solvent. 

On the other hand, the v term is, in one respect, different from the actual conditions ; 
it is vapour pressure in air when both solution and solvent are under the sum of the 
pressures of the atmosphere and their own vapour pressures, while the actual 
experiments are made when the two liquids are under the pressure of the atmosphere 
alone. It is thought that this slight difference may be neglected. 



Evaluation of the Integrals. 

f\+i> 
sete. It will be seen on p. 198 (Table IV.) that the coefficient of 
A+ ", w 

compression of any one solution varies but little at different pressures ; it was, 
therefore, thought that its mean value would be accurate enough for the purpose in 
view, and the following table gives the resulting volumes of the several solutions 
when under compression. Columns (1) and (2) are a repetition of those on p. 181 
(Table lA.) ; (3) gives the number of grammes of water to one gram-molecular weight 
of anhydrous salt ; (4) gives the observed equilibrium pressure, taken from a graph 
when necessary ; (5) gives the mean coefficient of compression per atmosphere, also 
taken from a graph when necessary; (6) to (12) give the volumes of the respective 
solutions which contain one gram-molecule of salt when under the pressure given 
at the head of the respective columns. 

The numbers in the horizontal line between the brackets have not been used in the 
reduction it was considered that the changes in volume were too small to give 
reliable results. 

On plotting the volumes in any one of the columns (6) to (12) against the figures in 
column (3), it will be seen that the resulting curve is practically a straight line, hence 
we may take the change in volume (at any given pressure) caused by a change in 
concentration due to the loss of one gramme of water as constant, and this volume 
ehange will be given by the ratio of the difference in volume divided by the 



OSMOTIC PRESSURES OF AQUEOUS SOLUTIONS OF CALCIUM FERROCYANIDE 201 



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VOL. CCIX. A. 



2 D 



202 THE EARL OF BERKELEY, MR. E. G. J. HARTLEY AND DR. C. V. BURTON : 

corresponding difference in column (3). This ratio is practically the s of the term. 
Further, it will be seen that the s for any given solution varies but slightly with the 
pressure. The maximum difference is only 0'5 per cent. It was, therefore, considered 
that for the purpose of evaluating the integral, sufficient accuracy would be attained 
if we put 

fA+;) fA + ;i 

s dp = 5 J dp. = s (P-TT,,,}, 

ait <nr 

where the mean value of s between the limits is s, obtained in the manner just 
indicated. 

These mean values are given in the following table* : 



Weight 




Weight 




Weight 




concentration. 




concentration. 




concentration. 




49-966* 


0-956 


42-889 


0-967 


31-388 


0-977 


47-219 


0-959 


39-503 


0-971 







In Prof PORTER'S ideal apparatus, it will be rememl)ered that there is supposed to 
be a pressure p u on the pure solvent piston. In our actual experiments this p a 
vanishes ; hence p = P, so that the term under discussion becomes sP. 

[A+w, 

(2) The term ?< dp. As the specific volume of water at C. does not differ 



appreciably from unity, even over a pressure range of one atmosphere, this term, 
remembering that p = 0, reduces to TT M , which is a negligibly small quantity. 

(3) The term " v dp. There seem to be no data for the exact evaluation of this 

J ",m 

integral, but if we assume that both BOVLK'S law and the partial-pressure law apply 
to the vapour pressure of water in air, we may put 



( 7 

" V dp = -2 log, -5? = -2 log, -, 

J it On D^f. f i 



where 



3 a o = vapour density of water vapour in air when the water is under the pressure A + TT M , 
1 = observed loss of weight of the solution and water vessels, 
Z, = observed loss of weight of the solution alone. 

The original equation thus reduces to 



" The solution of weight concentration 49 966 is taken because it is the solution for which we have the 
lowering of vapour pressure. Sec p. 190, Table HA. 



OSMOTIC PRESSURES OF AQUEOUS SOLUTIONS OF CALCIUM FEREOCYANIDK 203 

On p. 341 of CASTELL EVANS' ' Phys. Chem. Tables,' the value of ir alt derived from 
REGNAULT'S measurements is given, together with the value of p a0 , which he has 
calculated from REGNAULT'S work on the assumption that the partial-pressure law 
holds.* Using these two values, the results tabulated below are obtained. 

By a similar process of evaluation of the integrals in Prof. PORTER'S equation 
[equation (1) on p. 177] it is easily seen that it reduces to 



where TT O is the vacuum vapour pressure of water and /a,, its vacuum vapour density, 
and taking BROCK'S recalculation of REGNAULT'S work on these two quantities in a 
vacuum, and assuming that they are applicable to the experiments, we obtain the 
results given below under the head of " unmodified" equation. 

TABLE VI. 



(1.) 


(2-) 


(3.) 


W 


Weight 
concentration. 


" Unmodified " equation. 


'' Modified " equation. 


Observed equilibrium 
pressure. 




atmospheres. 


atmospheres. 


atmospheres. 


49 966 


135-04 


131-45 


130 -66t 


47-219 


116-05 


112-96 


112-84 


42-889 


88-99 


86-61 


87-09 


39-503 


72-54 


70-61 


70-84 


31-388 


42-38 


41-24 


41-22 



The concordance of these numbers seems to indicate a satisfactory agreement 
between experiment and thermodynamic theory. 

* Private communication. 

t On turning to Table III., p. 191, it will be seen that a solution of weight concentration 50-184 gave 
an equilibrium pressure of 131 -04 atmospheres, while one of 49-913 gave 131-38 atmospheres. One of 
these two observations must evidently be in error. As the value for equilibrium pressure of the 
strongest solution given in the table is derived from the graph of this pressure against concentration, 
using the mean of these two observations as the ultimate point, it may be that the value given is 
0*5 atmosphere too low. 



2 D 2 



[ 205 ] 



IX. The Effect of Pressure upon Arc Spectra. No. 2. Copper, \ 4000 to X 4600. 

By W. GEOFFREY DUFFIELD, D.Sc., Honorary Research Fellow in Physics at 
the University of Manchester, Mackinnon Student of the Royal Society. 

Communicated by Prof. E. KUTHERFORD, F.R.S. 

Received September 1, Read November 5, 1908. 

[PLATES 10-11.] 

CONTENTS. 

Page 

1. Preliminary 205 

2. Apparatus 206 

3. Behaviour of the copper arc under high pressures 206 

4. The photographs 207 

(1) Method of exposure 207 

(2) Description of the plates 207 

5. The broadening of the lines 208 

6. The displacement of the lines 209 

(1) Method of measurement of the photographs 209 

(2) Table I. of the displacement 209 

(3) Table II. of the displacement 211 

(4) Displacement curves 212 

(5) Eelation between the pressure, displacement and wave-length 212 

(6) Mean values of the displacement 215 

(7) Displacement and reversal of lines 216 

(8) Two-fold value of the displacement t 216 

7. Changes in relative intensity under pressure 218 

8. Series of lines in the copper spectrum 219 

9. 100 to 203 atmospheres [Added October 23, 1908] 222 

10. Summary of results 225 

1. PRELIMINARY. 

THE effect of pressure upon the arc spectrum of copper was first investigated by 
HUMPHREYS and MOHLER,* who, in 1897, found that under pressures up to 
14J atmospheres the lines became broader and were displaced towards the less 
refrangible end of the spectrum. In 1907 photographs were obtained by 

* HUMPHREYS, ' Astrophysical Journal,' VI., p. 169 (1897). 
VOL. CCIX. A 449. 14.12.08 



206 DE. W. GEOFFREY DUFFIELD ON THE 

HUMPHEEYS* at pressures of 42 and 69 atmospheres, and measurements were made 
of the displacement of several lines at those pressures. 

The following is a more detailed discussion of the behaviour of the copper arc 
under pressure than has yet been published. The work has been confined to the 
region \ = 4000 to X = 4600 A.U., and the pressures have ranged from 1 to 203 
atmospheres, t 

2. THE APPAKATUS. 

The arc was formed between copper poles, diameter -| inch, within the pressure 
cylinder designed by Dr. PETAVEL, F.R.S., which had previously been used for the 
investigation of the effect of pressure upon the iron arc.J The light passed through 
the window in the side of the steel chamber, and was reflected by the mirror system 
(previously described), which enabled the image of the arc, which was very unsteady 
at high pressures, to be continually focussed upon the slit of the 21^-ft. Rowland 
Grating Spectroscope in the Physical Laboratory of the Manchester University. 

The Second Order Spectrum was employed, the dispersion being 1'3 A.U. per 
1 mm. 

An increase in pressure was obtained by the admission of air into the cylinder from 
a gas-holder, suitable valves and gauges being interposed. 

Direct current was supplied by the Corporation mains at 100 volts, the pressure 
being reduced to about 60 volts by a resistance frame ; when the copper arc was 
burning steadily under pressure the current was maintained at about 13 amps. 

3. THE BEHAVIOUK OF THE COPPER ARC UNDER HIGH PRESSURES. 

Under normal pressure the arc between copper rods was maintained with 
comparative ease, and up to 5 atmospheres pressure no difficulty was experienced 
with it, but at higher pressures it rarely burned for more than three or four seconds 
at a time, because the luminous metallic vapour which was expelled from it rendered 
it very unstable and frequently blew it out ; at these pressures a single exposure is 
the integrated effect of a number of short-lived arcs. 

Like the iron arc, the brilliance of the copper arc increases with the pressure of the 
surrounding air, the image of the arc upon the jaws of the slit becoming dazzlingly 
bright at 100 atmospheres. As far as could be gauged from visual observations the 
intensity increases continuously with the pressure. 

In spite of this increased brilliance there is no concomitant decrease in the 

* HUMPHREYS, ' Astrophysical Journal,' XXVI., p. 18 (1907). 

t The description of the work upon pressures above 100 atmospheres is given at the end of this paper 
(p. 222). It was added October 23, 1908. G. D. 

t W. G. DUFFIELD, 'Report Brit. Association York,' p. 481 (1906); 'Koy. Soc. Proc.,' A, 79, p. 597 
(1907); 'Phil. Trans.,' 208, p. Ill (1908). 



EFFECT OF PEESSUEE UPON AEC SPECTEA. 



207 



necessary time of exposure, because under pressure the lines broaden and the energy 
of vibration is spread over a greater area. 

Though the characteristic green appearance of the copper arc was observed at all 
pressures up to 100 atmospheres, the red flame which frequently issues from the 
normal arc appeared with great brilliance at 80 and 100 atmospheres.* 

At the conclusion of the experiments the copper rods were removed ; the lower was 
found to be coated with black oxide, and the upper with a fine grey deposit which is 
thought to be a basic nitrate. On the tips of the poles minute metallic globules had 
been formed ; these when first examined lacked the red lustre characteristic of copper 
and were of a silvery whiteness, but the red lustre appeared after some months. 

4. THE PHOTOGRAPHS. 
(1) Method of Exposure. 

As in the previous work with the iron arc, the comparison spectrum under at- 
mospheric pressure was photographed in the central strip of a plate with the spectrum 
under pressure above arid below it. To ensure that no accidental displacements were 
produced, the comparison spectrum was photographed both before ;ind after the one 
under pressure. The arc was operated by the writer and the mirrors by an assistant. 

The following photographs have been obtained : 



Atmospheres. 


Number of photographs. ! Atmospheres. 


Number of photographs:. 


5 


3 


50 


2 


10 


2 


00 2 


15 


3 


70 


i 


20 


3 


80 


2 


30 


2 


100 


1 


40 


3 







Plates : Imperial Flashlight. Developer : Imperial Pyro-Metol Standard. Expo- 
sure varied from 3 minutes at 5 atmospheres to 60 minutes at 100 atmospheres. 

(2) Description of the Plates. 

Plates 10 and 11 illustrate the behaviour of the copper arc under different pressures ; 
Plate 10 includes the region X = 4050 to X = 4300, and Plate 1 1 the region X = 4350 to 
X = 4600. The photographs, which are full-size positive reproductions of the originals, 
are arranged in order of increasing pressure from the top at 1 atmosphere to the 
bottom at 80 atmospheres, the central strip being always at normal atmospheric 
pressure. 

* [Note added October 23, 1908. Subsequent observations up to 200 atmospheres show that the arc 
becomes decidedly bluer at about 125 atmospheres, and nearly as white as a carbon arc at 200 atmospheres.} 



208 DR. W. GEOFFREY DUFFIELD ON THE 

To facilitate reference to the lines arbitrary letters have been assigned to them, 
beginning alphabetically at the more refrangible end ; a is not included in the portion 
reproduced, but its behaviour resembles that of the strong line d. 

The prominent features are : 

(1) The broadening of the lines, 

(2) Their displacement towards the red end of the spectrum, 

(3) The changes in relative intensity, 

(4) The obliteration of the series lines within the region examined, 

(5) The absence of reversals. 

Unfortunately the exposures were not sufficiently equal for a strict comparison of 
the reproduced photographs with one another to be feasible; but Plates 10 and 11 
illustrate the remarkable fact that at the highest pressures the lines d, Plate 10, and 
I, o, Plate 11, fail to impress the photographic plate, though they were originally 
amongst the strongest lines in the copper spectrum. 

The plates also show that the most intense portion of each line is displaced under 
pressure from the position it occxipies at normal pressure, the direction being that of 
increasing wave-lengths. Line^', at 70 and 80 atmospheres, affords a good illustration 
of this point, and, since this line is, when under pressure, completely on the right-hand 
side of the normal line, the phenomenon cannot be referred to an unsymmetrical 
broadening. 

Unlike the spectrum of the iron arc in this region, no reversals have been observed 
under pressure. 

5. THE BROADENING OF THE LINES. 
From the photographs we learn the following facts : 
In the region studied (X 4000 to X 4600) 

1. All lines broaden under pressure. 

2. The broadening increases with the pressure, but different amounts of exposure 
necessarily make it difficult to determine if the increase is continuous and linear with 
the pressure. 

3. The broadening of all the lines examined is unsymmetrical, being greater on the 
less refrangible side. 

4. The lines may be divided into two classes according to the nature of their 
broadening. Those of the first class become under low pressures so faint and hazy 
that they almost resemble bands (for example, d at 15 and 20 atmospheres, Plate 10) 
and under higher pressures are dissipated. Those of the second class, though very 
broad, remain more or less well-defined lines (Plate 10, i, Plate 11, j, n, p, q), some, 
however, diminishing in intensity until they fail to impress the sensitive plate (I, o, 
Plate 11). 

5. Those lines which are originally strongest are not necessarily the most broadened 



EFFECT OF PRESSURE UPON ARC SPECTRA. 209 

under pressure (j, p, Plate 11). No relation has l)een found between the original 
intensity of a line and its width under pressure. 

0. The magnitude of the broadening even for the well-defined lines may be as great 
as 8 A.U. under 100 atmospheres. 

7. The types of broadening of the nebulous and sharp non-series lines are very 
similar, but the latter are more sharply defined on their violet edges. They retain 
their characteristic " soft" and " hard" appearances throughout. 

8. In the neighbourhood of the 1st sub-series lines there is generally a cloudy 
appearance under pressure, as though there is some tendency of the vibrating system 
producing these lines to form a banded spectrum. This resembles in a modified 
degree the spectrum of the silver arc, most of whose lines vanish under pressure, 
giving place at low pressures to a banded or nebulous fluted spectrum, and at the 
highest pressure reached by the writer (200 atmospheres*) to a practically continuous 
spectrum. 

6. THE DISPLACEMENT OF THE LINES. 
(1) Method of Measurement of the Photographs, 

The Kayser Measuring Machine was used, the setting being always made between 
parallel threads as accurately as possible upon the most intense portions of the lines 
under pressure, and advantage was taken of the astigmatic property of the grating of 
narrowing a line at its extremities. Twelve settings were made upon each line on 
each plate, six with the plate in one position and six with it in the reversed position. 
When there was not good agreement between the readings this number was exceeded. 
The fuzziness and great breadth of the lines at 100 atmospheres made the setting ot 
the wires a matter of difficulty it was found simplest to prick the most intense part 
of each line upon the film before placing the photograph in the machine. 

(2) Description of Table I. 

Table I. shows the nature of the agreement obtained from the measurements of the 
same line on different photographs taken at the same pressure. 

The first column indicates the line, and the subsequent columns its displacement 
upon the different plates named at the head of the column, the mean values for each 
pressure being also given. The readings are in thousandths of a turn of the screw 
of the measuring machine, whose pitch is ^ mm. The drum-head is divided into 
100 divisions. 

The agreement is remarkably good at high pressures, but at low pressures the 
width of the line has increased in a greater proportion than the displacement, and the 
concordance is not so great. At 5 and 10 atmospheres there is little agreement 

between the plates. 

* Added October 23, 1908. G. D. 

VOL. CCTX. A. 2 E 



210 



DR. W. GEOFFREY DUFFIELD ON THE 
TABLE I. 





5 atmospheres. 


10 atmospheres. 


15 atmospheres. 


20 atmospheres. 










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157 


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262 


280 


271 


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331 


340 


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395 


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553 


h 
































i 


371 


155 








505 


263 





380 


417 


460 


391 


595 


590 


583 


589 


j 435 





. 


. 


533 


444 





390 


478 


646 


505 


695 


722 


700 


702 


/: 























487 


325 


406 





681 





681 


1 

'lit ' 





511 

















1282 





1282 





1310 





1310 


n ; 380 


107 








432 


297 





484 460 


503 


482 


610 


657 


590 


619 





620 





432 














617 


868 


725 


736 


1012 





1012 


P 

















455 








545 


700 


622 : 853 


761 


760 


791 


q 


554 


143 








655 


485 





637 


585 


770 


664 894 


815 


850 


853 


Each reading, which is in thousandths of a turn of the screw, is the mean of 12 separate measurements 


of the displacement. 


To reduce to Angstrom units these must be multiplied by 0-000431. 




30 atmospheres. 


40 atmospheres. 


50 atmospheres. 


60 atmospheres. 








00 








CO 






w 






BB 
















<D 












9 








S 






* 






CO 


J3 




c*i 


a 




CO 


OO 


c 










id 














w 






W 


W 


S 


> 


K 


w 


> 


H 


W 


> 




-2 


-4-> 


eg 


S 


-2 


1 


I 


43 


q 


a 

eg 


S 


S 









cfl 


CO 


a 


eg 






cS 


r 


CD 


CO 









K 


S 


s 


K 


PH 


PM 


% 


S 


S 


^ 


S 


K 


^ 


[6Pb 




570 


570 




580 


485 


533 




961 


961 


922 


1140 


1031] 


f 








- 























1490 


1760 


1625 


(J 

















935 


935 











1317 


. 


1317 


h 














. 

















1515 


1760 


1637 


i 


837 


709 


768 


749 


1079 


963 


930 


1219 


1259 


1239 


1680 


1472 


1576 


j 


841 


880 


860 


897 


1408 


1030 


1112 


1372 


1653 


1512 


1730 


1708 


1719 


k 


. 























1540 


1540 


1390 


2070 


1730 


I 


870 





870 
































m 
































860 


970 


915 


n 


725 


855 


790 


923 


1170 


1180 


1091 


1500 


1560 


1530 


1573 


1797 


1685 





. - 














2340 


2340 








. 


3050 





3050 


P 


978 


1055 


1016 


1159 


1502 


1180 


1280 


1757 


1835 


1796 


1890 


1895 


1893 


1 


917 


1123 


1020 


1133 


1645 


1463 


1414 


1875 


1917 


1896 


2152 


2192 


2172 



* Mean of 24 measurements of the displacement of each line. 

1" J! I! 



EFFECT OF PRESSUEE UPON ARC SPECTRA. 
TABLE I. (continued). 



211 





70 atmospheres. 


80 atmospheres. 


100 atmospheres. 


Plate E6. 


Plate E4. 


Plate El 2. 


Mean values. 


Plate 13. 


[JPb 


803 


1028 





1028 


-] 


e 





1130 





1130 




f 


1610 


1700 





1700 





g 


1450 


1862 





1862 





h 


1930 


2320 





2320 





i 


1817 


1917 


1985 


1951 


2109 


j 


1880 


2170 





2170 


2429 


k 


1980 


2000 





2000 


. 


I 


. 














m 


840 


1360 


. . 


1360 





n 


1906 


2196 


2300 


2248 


2769 




















P 


2271 


2592 


2550 


2571 


3021 


<1 


2332 


2630 


2623 


2627 


3020 



(3) Description of Table II. 

Table II. gives in Angstrom units the mean value, of the displacement at each 
pressure. The first column contains a list of the arbitrary letters assigned to the 
different lines. The second column gives the wave-lengths of the lines according to 
KAYSER and RUNGE'S tables. The subsequent columns show the displacements of the 
lines at different pressures in Angstrom units. The displacement is in each case, 
towards the side of greater wave-length. The pressures are the excess above one 
atmosphere. The measurements in brackets, which were made by dotting the plates, 
have not been plotted in the diagram. 

TABLE II. 





X. 


5. 


10. 


15. 


20. 


30. 


40. 


50. 


60. 


70. 


80. 


100. 


[iPb 


4058-04 


O2 


i 


0-117 


0-144 


0-246 


0-230 


0-414 


0-444 


0-346 


0-443] 


Pb 


d 


4063-50 


-a 



JS 
CL, 


0-464 


























e 


4123-38 





s 











. 





. 





0-487 





f 


4177-87 


W> 
o 


1 


0-220 


0-294 











0-700 


0-693 


0-733 





y 


4249-21 


4$ 

O 


+5 




0-189 


0-238 





0-403 





0-568 


0-625 


0-803 





h 


4259-63 


ft 
&t 


PH 

















0-706 


0-832 


0-999 





i 


4275-32 


g 


a 

03 


0-168 


0-254 


0-331 


0-401 


0-534 


0-679 


0-783 


0-841 


0-909 


j 


4378-40 


* 


O> 

> 


0-218 


0-303 


0-371 


0-479 


0-652 


0-741 


0-810 


0-935 


1-047 


k 


4415-79 


4a 

0> 


.13 

O 


0-175 


0-294 








0-664 


0-746 


0-853 


0-862 





I 


4480-59 


,0 


rO 


(0-553) 


(0-565) 


(0-375) 




















m 


4507-62 


-4-2 

a 


*3 

a 

















(0-394) 


(0-362) 


(0-586) 





n 


4509-60 


g 


1 


0-208 


0-267 


0-341 


0-470 


0-685 


0-779 


0-862 


0-960 


1-190 





4531-04 


Q 




o 

ID 


0-317 


0-436 





1-009 





1-314 











P 


4539-98 


M 


IP 


0-268 


0-341 


0-438 


0-552 


0-774 


0-816 


0-979 


1-108 


1-302 


q 


4587-19 





o 


0-286 


0-367 


0-440 


0-609 


0-817 


0-936 


1-005 


1-132 


1-302 


*d-2 


4074-55 


K 


fc 


0-129 








" " ' 


" 


~~ r " " 


" 


_ 


~ 



o 

Displacements are in Angstrom units. 

* Impurity (?). 

2 E 2 



212 



DR. W. GEOFFKEY DUFFIELD ON THE 



(4) The Displacement Curves. 

The values of the displacements given in Table II. have been plotted in Diagram 1, 
in which abscissae represent the excess of pressure above 1 atmosphere, and ordinates 
the increase in wave-length of the lines in thousandths of an Angstrom unit. 

Each line on the diagram represents the behaviour under pressure of one spectral 
line, which may be identified by the letter attached to it. Small arrows indicate 
those pressures at which measurements have been made. Dotted lines connect 
isolated observations. 



1300 

I2OO 

5 1100 

E3 

2 1000 

So 

cjjj 900 



DIAGRAM I. 




Pb 



Pressures in atmospheres (excess above one atmosphere). 



(5) The Relation between the Pressure, Displacement, and Wave-length. 

(1) Non- Series Lines.*- The increase of the displacement with the pressure is 
shown in Diagram 1, and for each non-series line is continuous and linear within the 
accuracy of the measurements. At low pressures (as we have seen) the displacements 
on different plates are too discordant to be plotted, they are generally greater than 
they should be if the linear law is to hold good, but, for the reason already pointed 
out, that at 5 and 10 atmospheres the broadening seems proportionately greater than 
the displacement, these measurements are not considered so reliable as the ones under 

* Not belonging to the Principal, First or Second Subordinate Series. See p. 219. 



EFFECT OF PRESSURE UPON ARC SPECTRA. 



213 



higher pressures. The high value of the displacement may, perhaps, be referred to 
the phenomenon discussed on p. 216, 8. 

The rates of increase of the displacements with the pressure vary greatly for 
different lines. On the assumption that the displacement is a linear function of the 
pressure, the displacement per 1 atmosphere has been calculated for each line between 
pressures of 30 and 100 atmospheres, by dividing the measured displacement by the 
number of atmospheres, and the results are given in the following table : 

TABLE III. Displacement per Atmosphere in Thousandths of an Angstrom Unit.* 





Wave-lengths. 


30. 


40. 50. GO. 


70. SO. 


100. Mean. 








, 






] 


[ft Pb 


4058-04 


8-2 


I i 
5-7 8-3 7-4 


4-9 


5-5 


G-7] . 


g 


4249-21 





10-1 9-5 


8-9 


10-0 


9-6 


i 


4275-32 11-0 10-0 10-7 11-3 


11-2 


10-5 


9-1 10-5 


j 


4378-40 12-4 12-0 13-0 12-3 


11-6 


11-7 


10-4 11-9 


n 


4509-60 11-4 11-7 13-7 13-0 


12-3 


12-1 


11-9 12-3 


P 


4539-98 


14-6 


13-8 15-5 13-6 


14-0 


13-8 


13-0 14-0 


1 


4587-19 


14-7 


15-2 16-3 15-6 


14-3 


14-1 


13-0 14-7 


For tl, 1, o the displacements per atmosphere are doubtful; for d we get the value 31 -0 at 


15 atmospheres; for / the values 37, 37'5 and 12'5 at 15, 20 and .'SO atmospheres respectively, mean 


= 29; and for o the values 21 1, 21 -8, 25- 2 and 21 '9 at 15,20, 40 and (50 atmospheres respectively, 


mean =22' 5. 





The last column gives the mean value of the displacement per atmosphere, and it is 
at once apparent that these values increase with the wave-length. HUMPHREYS! has 
suggested that these two quantities are dependent upon one another, and, though for 
the investigation of this relationship the range of wave-length is small, the above 
table supports that view. 

The precise nature of the relation between them is difficult to determine and may 
be discussed from two different standpoints : 

(a) In Diagram 2 the average displacements per atmosphere are shown as 
ordinates and the wave-lengths as abscissae. The graph which is obtained is approxi- 
mately linear, and it also satisfies the requirements of line b due to lead ; it is seen to 
point to about 3600 as the wave-length of the line which would not be displaced 
under pressure ; but the work of HUM PHREYS, who has observed displacements of 
lines with a smaller wave-length than 3600 A.U., indicates that this graph cannot 
accurately represent the behaviour of the copper lines throughout the spectrum. 

* Measurements at 5, 10, 15 and 20 atmospheres are not included because their accuracy is not as great 
as those made at higher pressures, nor are the readings for the faint lines /, h, k, which were measured by 
dotting the film throughout the whole range. 

t HUMPHREYS, ' Astrophysical Journal,' VI., p. 169 (1897). 



214 



DR. W. GEOFFREY DUFFIELD ON THE 





1 




c 




o 




d 




Wave-length. 


Mean. 


a 












1 


1> 4058- 


04 


67 


OH 




n 


4249- 


21 


96 




i 


4275- 


32 


105 


cS 


j 


4378- 


40 


119 





n 


4509- 


60 


123 


ft 


P 


4539- 


98 


140 


s 




4587- 


19 


147 


I 










o 




a 




"O 




S 



160 



I2 



100 



60 



3 60 



40 



DIAGRAM 2 




COPPER 



LEAD 

x ft 



4000 4200 4400 

Wave-lengths in Angstrom units. 



460O 



If we assume that the origin is on the curve representing this relation, we are 
forced to the conclusion that the displacement varies with a higher power of the 
wave-length, and Table IV. shows the calculated values of the constants on the 
assumptions that the displacement varies as the 1st to the 7th powers of the wave- 
length. 

TABLE IV. 





A 


d 


A 


A3 


A 


A" 


A-' 


A 


\" 








d' 


d ' 


d ' 


d ' 


d' d' 


d ' 


ff 


4249-21 


9-6 


443 


188 xlO 4 


799 x 10 7 


339 x 10 n 


144x 10 15 


612 xlO 18 


260 x 10 22 


I 


4275-32 


10-5 


407 


174 744 


318 136 


581 


248 


j 


4378-40 


11-9 


368 


161 


705 


309 , 135 


591 


259 


n ! 4509 60 


12-3 


367 165 745 


336 ; 152 


685 


309 


P 


4539-98 


14-0 


324 


147 


667 


303 138 


626 


284 


q 


4587-19 


14-7 


312 


143 


656 


301 


138 


633 


290 


Mean constants .... 


370 


163 


719 


318 


140 


621 


275 


















Maximum percentage de-~l 
viation from mean . . J 


per cent. 

19-7 


per cent. 

15-3 


per cent. 
11-1 


per cent. 
6-6 


per cent. 

8-6 


per cent. 

10-3 


per cent. 

12-4 



The smallest maximum deviation appears for the 4th power of the wave-length. 
For higher powers there are abnormally high values for the line n ; omitting these 
from the last three columns the values are : 



EFFECT OF PRESSURE UPON ARC SPECTRA. 



215 



Constants 



Maximum deviation , 



d ' 
138 

per cent. 

4-3 



x A; 

d' d' 

608 268 



per cent. 
4.4 



per cent. 

8-2 



In this case the best agreement appears when the displacement varies as the 5th or 
6th power of the wave-length. 

(2) Series Lines. Table I. also gives the few measurements which were possible of 
the lines belonging to the 1st and 2nd subordinate series. They are not sufficiently 
numerous, nor is their accuracy sufficiently great, to determine the pressure- wave- 
length-displacement relationships. 

(6) Mean Values of the Displacement. 

Taking the mean value of the displacements of these copper lines at each pressure, 
the following numerical values are obtained : 



Atmospheres 


15 


20 


30 


40 


50 


GO 


70 


80 


100 




Mean displace-"! 
ments . . J 


236 


315 


383 


486 


692 


752 


844 


965 


1150 


r Thousandths of <in 
I Angstrom unit. 




IO 20 30 40 SO 60 70 30 

Pressures in atmospheres (excess above one atmosphere). 



90 



IOO 



These values are plotted in Diagram 3. The mean displacement per atmosphere 
of all copper lines fully examined is 12 - 2 thousandths of an Angstrom unit ; it is 
probable that extension into the longer wave-lengths would increase and extension 



216 1>R. W. GEOFFREY DtfFFIELD ON THE 

into shorter wave-lengths diminish this value. The mean displacement per atmosphere 
of the lead line is 6'7 thousandths of an Angstrom unit (a little more than half that 
of the copper lines) ; its values at different pressures are plotted on the same diagram. 

(7) Displacement and Reversal of Lines. 

The displacement curves for iron suggested a departure from the linear relationship 

at those pressures at which a large number of reversals appeared. In the case of 
copper no reversals have been found between X 4000 and X 4600, and the displacement 
varies directly with the pressure within the accuracy of the experiment. 

(8) The Two- fold Value of the Displacement? 

Comparison of the values of the displacements given in Table IT. with those of 
previous workers affords additional evidence in support of the reality of the 
phenomenon to which the writer first drew attention in his discussion of the iron arc 
under pressure,* where it was shown that at certain pressures two values sometimes 
appeared to exist for the displacement of a line. In the case of iron all the lines 
belonging to the same group were upon one plate sometimes displaced twice as much 
as they were upon others at the same pressure. Sometimes all three groups showed 
abnormally high values, sometimes Groups II. and III., and at others Group III. 
alone showed them. Whatever the nature of the disturbing cause, Group III. and 
then Group II. seemed most susceptible to it. The ratios of the values of the 
displacements at 25 atmospheres for different plates were : 

Group III. . . . Reversed lines 2 - 0, 

Group III. . . . Non-reversed lines . . . 1'8, 

Group II. . . . Non-reversed lines . . . 2'0, 

Group I Reversed lines 1'8. 

In the iron spectrum the phenomenon made its appearance in the neighbourhood of 
25 atmospheres, where, because the displacements are not very large, and because of 
the unexpected nature of the occurrence, some doubt was felt about it. But the 
remarkable fact that the displacements of the copper lines measured by HUMPHREYS 
at 69 atmospheres are half the values of the displacements at 70 atmospheres in the 
present investigation lends some support to the writer's original view that at certain 
pressures some lines may have two values of the displacement : within the limits of 
error of measurement one is twice that of the other. It is true that HUMPHREYS 
has only measured each line twice and that only six lines have been measured in 
common, but the magnitude of the discrepancy should be quite beyond the limits of 
error of measurement. It must also be remarked that HUMPHREYS and the writer 

* DUFFIELD, 'Phil. Trans.,' A, 208, p. Ill (1908). 



EFFECT OF PRESSURE UPON ARC SPECTRA. 



217 



may differ by 50 per cent, in judging which is the most intense portion of a line and 
that the discrepancy may possibly be explained in this way. The probability that 
this is the explanation is not great, because measurements of the writer's photographs 
made by different observers do not differ materially from one another. 

The following table gives all previous measurements of the copper lines under 
discussion, together with a comparison with the writer's values. It will further be 
seen that at 7 atmospheres on HUMPHREYS' plates the rate of displacement is twice as 
great as it is at 69 atmospheres, the only exception being that of line q (A. = 4587'19), 
but the values at low pressures are not always very reliable, and the writer does not 
wish to lay too much stress upon this line of argument. 



TABLE V. 





\ A. 


B. 








Previous measurements. 


Present 
measurements. 


Ratio B/A. 




A. 












7 
atmospheres.* 


69 
atmospheres, t 


70 
atmospheres. 


CO T 
,-j-, > atmospheres. 


/ 


4177-87 


87 


_ 


693 


_ 


g 


4249-21 


57 


273 


625 


2-3 


h 


4259-63 





387 


832 


2-1 


i 


4275 32 


64 











j 


4378-40 


81 


420 


810 


1-9 


k 


4415-79 


80 


409 


853 


2-1 


I 


4480-58 


50 














4531-04 


53 











P 


4539-98 


459 


979 


2-1 


1 


4587-19 74 


513 


1005 


2-0 



The displacements are in thousandths of an Angstrom unit. 

Upon what factor the value of the displacement is most directly dependent it is 
difficult "to determine. In the writer's own experiments with the iron arc the chief 
variables were the current strength and the length of the arc which, on account of 
the necessity for continually striking the arc, could riot be kept constant. The 
variables dependent upon these are the temperature, potential gradient, the quantity 
and, perhaps, the density of the material in the arc. The nature of the poles used by 
HUMPHREYS in obtaining his copper arc at 69 atmospheres is not specifically stated nor 
is the current strength,! but the voltage of his supply was 220 whereas that used for 

* HUMPHREYS, ' Astrophysical Journal,' VI., p. 169 (1897). 
t HUMPHREYS, 'Astrophysical Journal,' XXVI., p. 18 (1907). 

[I No differences in the displacements at 70 atmospheres were found when the voltage of the supply 
was 100, 200, or 400 volts. Added October 23, 1908.] 
VOL. CCIX. A. 2 F 



218 DR. W. GEOFFREY DUFFIELD ON THE 

the present experiments was 100 volts. The differences are quite possibly due to 
different amounts of metallic vapour being present in the arc in the two cases.* 

The hypothesis that the vibrating systems consist of pairs of similar particles which 
under certain conditions dissociate is suggested, but the system must be such that its 
period of vibration is not radically altered by the dissociation. 

In connection with this phenomenon attention may be called to the anomalous 
behaviour of unsymmetrically reversed lines in the iron arc, in which the reversed 
parts are displaced half as much as the non-reversed line. It is possible that the 
conditions in the outer layers of the arc correspond to those that hold in the core 
when giving the lower value of the displacement. 



7. CHANGES IN RELATIVE INTENSITY UNDER PRESSURE. 

As the pressure is increased the relative intensities of the lines change. For 
broadened lines the intensity is an indefinite term, and the energy of the radiating 
system which gives rise to the line is better represented by the total photographic 
action upon the film than by the value of its maximum intensity. The energy 
emitted under pressure by the system responsible for the very faint hazy bands 
(a, 4022''83 ; d, 40G3'50, Plate 10) is a specially uncertain quantity, because the 
energy, though small for each element of the band, is spread out over a comparatively 
large area. 

The lines that have become obliterated under pressure have become so by one ot 
two processes, they have either remained fairly definite lines whose intensity has 
gradually diminished with increase of pressure (I, 4480'59 ; o, 4531'04, Plate 11), or 
they have been dissipated and become faint bands (d, Plate 10) whose intensity is not 
sufficient under higher pressures to affect the plate. In the first case the vibrating 
system seems to have gradually sunk to rest, in the second it appears to have suffered 
some violent disintegration. The obliterated lines belong to either the First or 

* An attempt was made to test this by using a 50 per cent, alloy of silver and copper. With some 
difficulty a photograph was taken at 70 atmospheres, but only one line, i (A = 4275), could be satisfactorily 
measured. Although its displacement is rather less than that of the same line when the pure metal is 
employed, the value was not a simple fraction of the other. 

For the pure metal the displacement was .... 0-783 A.U. (mean of 12 readings), 
For the alloy the displacement was -650 A.U. ( 24 ). 

The value for the pure metal is rather higher than is indicated by the average displacement per atmosphere 
over the whole range ; this is 10-5 thousandths of an Angstrom unit, making the calculated value for 
70 atmospheres = 0-735 A.U. This is also greater than the displacement of the alloy line. It is difficult 
to measure the displacements at these pressures with great accuracy, but such small evidence as we possess 
points to the displacement in the alloy being if anything smaller than in the pure metal. The values are, 
however, not simple multiples of one another, as in the phenomenon under discussion. It is also doubtful 
if it is the density that is the determining factor. 



EFFECT OF PEESSUKE UPON ARC SPECTRA. 



219 



Second Subordinate Series : the triplet a, c, d, that is dissipated, belonging to the First 
Subordinate Series, and the pair I, o, showing a gradual loss of intensity, belonging to 
the Second Subordinate Series. 

Table VI. gives those lines that are strengthened and weakened under different 
pressures. With the exception of the lines a and d of the First Subordinate Series 
the rule holds that the nebulous lines are strengthened and the sharp ones weakened 
under pressure. 

TABLE VI. 





A. 




5 


10 


15 


20 


30 


40 


50 


fiO 


70 


80 


100 


































ft 


4022-83 


N 


w 


w 


w 


w 




w 


vv 


w 




w 


w 


1st sub-series (oblite- 






























rated). 


[* 


4058-04 


S 


w 





w 


w 


w 


w 





w 


w 





w] 


Pb. 


t: 

d 


4062-94 
4063-50 


s \ 

N; 


w 


\v 


w 


w 


w 


w 


vv 


w 


w 


vv 


vv 


{1st sub-series (oblite- 
rated). 


fdl 


4072-10 




st 





st 


st 





st 








st 










*{<12 


4074-55 





st 





st 


st 





st 








st 










e 


4123-38 


N 











st 











st 


st 


st 







f 


4177-87 


N 


st 





st 


st 





st 





st 


' 










(1 


4249-21 


S 





w 


w 


w 


w 


w 


w 


w 


w 


w 







h 


4259-63 


N 


st 


st 


st 


st 





st 


st 


st 


st 


st 







i 


4275-32 


S 





w 


w 


w 

















. 







J 


4378-40 


N 


st 


st 


st 


st 


st 


st 


st 
















k 


4415-79 


N 


st 





st 


st 





st 


st 


st 


st 


st 







I 


4480 59 


S 


vv 


w 


w 


w 


vv 


w 


w 


w 


w 


w 


vv 


2nd sub-series (oblite- 






























rated). 


m 


4507-62 


N 


st 


st 


st 


st 


st 


st 


st 


st 


st 


st 


st 




n 


4509 60 


S 


w 


w 


w 


st 





vv 








st 













4531-04 


S 


w 


vv 


w 


w 


w 


w 


w 


w 


w 


w 


vv 


2nd sub-series (oblite- 






























rated). 


P 


4539-98 


N 


st 


st 


st 


st 


st 


st 


st 


st 





st 


st 




1 


4587-19 


N 


st 


st 


st 


st 
























































N = nebulous ; S = sharp ; st = strengthened ; vv = weakened. 

c and d have the appearance of a sharp superposed upon a nebulous line at 
atmospheric pressure, they are merged together at higher pressures, and finally vanish 
together. 

There is no sign whatever on any of the plates under pressure of the lines given by 
BAXENDALL! as enhanced at 454510 and 45 56 '10. 



8. SERIES OP LINES IN THE COPPER SPECTRUM. 

KAYSER and RUNGE,} who investigated the frequency relationships between the 
lines of the copper arc spectrum, besides finding several pairs with constant frequency 

* Due to impurities (?). Not given by KAYSER and RUNGE. 

t Publications of Solar Physics Committee, 'Tables of Wave-lengths of Enhanced Lines,' 1906. 
| KAYSER and RUNGE, ' Uber die Spectren der Elements,' 5, pp. 8-17. 

2 F 2 



220 



DK. W. GEOFFREY DUFFIELD ON THE 



p> 

H 

CQ 

H 





CO , 


-^ -> 




.5 1 3 J If 


^_ CO IO OS ^ CO >Q O t 


. 


'fl ^O ""a., ^ ^ 


|>-i OS O^-ilcslcMO,-!^-* 


1 


| 3*1," 


C^) t-H r t O3 i t O( ' r 1 




G 


CD O 

43 So 


^^? ^ ^ 





fe -W 1g 0> 


333 3 3 1 


a 


5 'ft 
,Q O cO 


OOO O O 


O 


rt 




j 


0} o 




a 
o 


5 n 

bC ^ 


sfe^-g-g-s-Sii-S-Sis-S - 


*P^ 


^ 




CO 






CO 


J- 




1 


O) , J 3 
C P- H 
fcJ 0) r^ 


.On. . -ft-ft- ^ I 'B H & 1 ' ' 




|11 


ij!!idiijjdl 


^ 


j-5-s^ 


i oj o2_ aj 02 i ;/:; 02 


f-4 

O 


c * ft 


P t p i Cu PH p 1 p i 


* 


s w " 




"b 






X 


c8 '" **< 


J J J : . ; 


W 


O O ^ p | 


PH PH PH PH' PH' PH 


S 


1 ' 




CO 


-f 





CO 


"3 s 


o o - 




'S 2 








'^ tS 


C 
_O 


ft ^ 


~ - tH tT 


"cS 


J 


^5 -^ 


J5 


-i 

A 




O 


o 




X 


0- 




2 


1-f '' 


1C t O t 

T . . 


<D v: 


PH S *0 


1 1 I-H O O 


.gAn 


02 rt 




S i 


"! , j 




2p 

h3 


o a C 

2 S 

Cog 


CO CO II * CO 



* 






a 

O 



8> 

SPad 



a 





W) 










1 



- 



O K 
C_J a) 

T3 .S 

V 



s 

I 

i 
s 

" 
a 

o 

"* M 

J3 V 

c 

> 

W) 

C CO 

g 

^3 O 

' 

tT T! 

CD a 



,3 c 

fl 

.2 -i 

-^> c 

o . 

s < 

-s 1 



f| 

(D cfi 

|.2 



S - - 
P-i ,-^j M 



hn SS ^ 
;ir P^ p^ 
g cc co 

ill 

Ooo 

o ce S 

.223 
o C C 
i 2 

g S S 
cl S S 

^300 

o o o 



i 
e 



lac 



e .-g 



S ft 



3 1 



g g 



H O 



EFFECT OF PKESSURE UPON ARC SPECTRA. 221 



differences, separated from the rest of the spectrum three series of lines the frequencies 
of whose members could be represented by three formulae ; these series have become 
known as the Principal, First and Second Subordinate Series. 

The Zeeman effect affords another means for their classification, and investigations* 
have shown that, though the pairs belonging to any particular series in the copper 
spectrum behave similarly in the magnetic field, there are marked differences between 
the behaviour of individual members of each pair. 

KiNGt has subjected the arc and spark spectra of copper to an exhaustive analysis, 
and, from the behaviour of the lines in arcs of different current strengths and sparks 
under various conditions, resolved them into three groups, which, however, do not 
correspond to those found by KAYSER and RUNGE. 

From their behaviour under pressure we possess an additional means for separating 
the lines of the copper spectrum into groups. HUMPHREYS^ first suggested this : 
chronicling three series with " small," " medium," and " large " shifts respectively. 

Table III. shows that the displacements of the series lines d, I, o are greater than 
those of the non-series lines, but the former lines are too broad for accurate measure- 
ments, and with the copper spectrum there is not the same distinct division into groups 
according to the amount of the displacement that is possible with the iron arc ; the 
nature of the lines and their changes of relative intensity afford the best means for 
classifying them. 

1. The nebulous and sharp lines retain their respective types throughout the range 

of pressure, 1 to 101 atmospheres. 

2. The nebulous non-series lines are strengthened under pressure relatively to the 

sharp lines. 

3. The four members of the recognised series (1st and 2nd sub-series) are weakened 

under pressure, and at the highest pressure are obliterated. 

4. The two members of the 1st sub-series pass through the stage of being faint 

hazy bands, and then as the pressure is increased are completely dissipated. 

5. The two members of the 2nd sub-series gradually diminish in intensity without 

abnormal widening, ultimately becoming obliterated. 

A comparison of these results with those of A. S. KING are of interest. KING has 
investigated the spectra obtained from different parts of the copper arc and spark, 
and has found that some lines occur more strongly near the poles and others more 
strongly in the centre of the arc or spark. The writer, || in a subsequent investigation 
of the iron arc, found some value in designating the former " polar" and the latter 

* RUNGE and PASCHEN, ' Astrophysical Journal,' XVI., p. 123 (1902). 
t A. S. KING, ' Astrophysical Journal,' XX., p. 21 (1904). 
I HUMPHREYS, 'Astrophysical Journal,' VI., p. 169 (1897). 
DUFFIELD, 'Phil. Trans. Roy. Soc.,' 208, p. Ill (1908). 
|| DUFFIELD, ' Astrophysical Journal,' XXVII., 260 (1908). 



222 DE. W. GEOFFREY DUFFIELD ON THE 

" median" lines, and this classification is of some use in co-ordinating KING'S results 
with those obtained in this research. In Table VII., PA = polar lines in the arc 
spectrum, PS = polar lines in the spark spectrum, and it will be seen that the PA 
lines are weakened under pressure and the PS lines strengthened. With the possible 
exception of the lines of the 1st sub-series of KAYSER and RUNGE these correspond to 
the sharp and nebulous lines respectively. The table contains a resume of the work 
that has been done upon this part of the spectrum for the purpose of classifying the 
lines. 

It is interesting to note that in the copper arc spectrum no marked differences 
have been observed in the behaviour of individual members of a pair under pressure 
as have been found to exist in a strong magnetic field, and, though there is some 
apparent structure on the wings of line d at 20 atmospheres, it is not certain that it 
is not due to irregularities in the ruling of the grating. 

KING'S conclusion that the weakening of the series lines in an atmosphere of 
oxygen* is due to diminished vapour pressure is not confirmed by their disappearance 
at high pressure. 

9. 100 TO 203 ATMOSPHERES. 
[Added October 23, 1908.]. 

The importance of extending the range of pressures was urged upon me by the 
unexpected behaviour of the silver arc under pressure, already mentioned paren- 
thetically in the present paper (p. 209), and it seemed of great interest to examine if 
an increase of pressure would similarly cause the copper line spectrum to vanish and 
give place to a banded spectrum. This possibility was held to justify the extension 
to higher pressures. 

The cylinder had originally been tested up to 400 atmospheres (liquid pressure) 
with a metal screw in place of the glass window. A second test, with the window in 
position, was made up to 350 atmospheres (liquid pressure). The glass held 
satisfactorily, but was too much strained when the pressure was reduced for objects to 
be clearly seen through it. In the hope that fused quartz would be less affected, a 
window of that material was inserted in the window-tube and air admitted to the 
cylinder from two gas-holders, the first being pumped up to 120 atmospheres and the 
second to 200 atmospheres. 

A fair photograph was in this way obtained at 185 atmospheres, but the quartz 
window chipped to such an extent under the combined action of the pressure and the 
heat from the arc that it was useless for subsequent experiments. A third window 
(also of fused quartz) was next employed, and with the aid of a third gas-holder 
(kindly lent by Mr. Chas. W. Cook, of the Manchester University Engineering 
Works), containing air at 210 atmospheres, 200 atmospheres were obtained within 

* A. S. KING, ' Astrophyeical Journal,' XVIII., p. 129 (1903). 



EFFECT OF PRESSURE UPON ARC SPECTRA. 223 

the pressure cylinder. The insulated stuffing-hoxes, which are the special feature of 
Dr. PETA.VEL/S cylinder, worked so excellently that the pressure only dropped 
15 atmospheres in 24 hours. 

Using a wide slit, three photographs of the copper spectrum, under 200 atmospheres, 
were taken with exposures of about 1 J hours each. 

When the pressure was reduced the window-tube was removed and examined. 
The quartz was at first as clear as when placed in position, but gradually small 
splinters extended across and through it, and faint metallic "pings" could be heard 
as the strain was released. The window thus became gradually less and less 
transparent until, after some hours, it scarcely allowed light to pass through, and 
when finally removed from the window-txibe it was in several pieces. This rapid loss 
of the windows has made the high-pressure work tedious and expensive. In 
subsequent experiments glass windows have proved more satisfactory, though thev, 
too, chip, however carefully the pressure may be released frequently a matter of 
two or three hours. 

The Photographs. 

In addition to the photographs enumerated upon p. 207, single photographs have 
been obtained in region X 4000 to X 4600, at pressures of 125, 150, 175, and 203 
atmospheres. The exposure varied from 40 minutes at 125 to 90 at 203 atmospheres. 
Photographs were also taken at 200 atmospheres with a small 1 -metre grating 
spectrograph. These afford valuable confirmation of the results obtained with the 
21^-ft. Rowland grating. 

General Features of the Results, 100 to 200 Atmospheres. 

No discontinuity in the nature of the spectrum was observed ; it remains a line 
spectrum up to 203 atmospheres, though there is some continuous spectrum from the 
poles of the arc. 

Broadening, The lines are broader, but the broadening does not seem to increase 
as fast as the displacement this is especially difficult to estimate at the highest 
pressures, because there is some general fogging due to scattered light in the room 
consequent upon a long exposure, and also because there is some continuous spectrum 
from the hot poles of the arc. 

Displacements. In the accompanying Table VIII. are given the measurements 
made at the pressures named at the top of each column ; and Diagram 4 shows the 
relation between the pressure and displacement throughout the whole range. Though 
the readings between 100 and 200 atmospheres are rather lower than were expected 
from the previous measurements, the difficulty in making the former is sufficient to 
account for the slight apparent departure from a linear relationship between the 
pressure and the displacement. 



224 



DR. W. GEOFFREY DUFFlELD ON THE 



TABLE VIII. 





A. 


125 atmospheres. 


150 atmospheres. 


203 atmospheres. 


/ 


4177-87 


1-319(1) 


l-263(?) 


2-030(?) 


. 9 


4249-21 


1-181 








h 


4259-63 1-073 








i 


4275-32 1-104 


1-233 


1-595 


3 


4378-40 


1-194 


1-181 


1-806 


k 


4415-79 


1-086 


1-284 





n 


4509-60 


1-293 


1-306 


1-677 


P 


4539-98 


1-241 


1-461 


1-935 


1 


4587-19 


1-237 


1-302 


1-698 



Displacements are in Angstrom units. 



200 



DIAGRAM 4 . 




Pressures in atmospheres (excess above one atmosphere). 

Changes in Relative Intensity. The series lines, all of which were obliterated 
below 100 atmospheres, do not reappear between 100 and 203 atmospheres, and the 
strengthened and weakened lines do not differ from those given in Table VI. (p. 219). 

The Colour of the Arc. As has already beeii stated, the arc is green at normal 
pressure, and this colour characterises the arc up to 100 atmospheres, when it appeared 
bluer ; this colour became less pronounced as the pressure was increased until at 
203 atmospheres it appeared blue-white, like a carbon arc. 

The Brightness of the Arc. The increase in brilliance with pressure, though 
noticeable between 100 and 200 atmospheres, was not so striking as between 1 and 
100 atmospheres. 



EFFECT OF PRESSURE UPON ARC SPECTRA. 225 

10. SUMMARY OF RESULTS. 

The spectrum of the copper arc in air has been examined in the region X = 4000 to 
X = 4600 A.U. at the following pressures 5, 10, 15, 20, 30, 40, 50, 60, 70, 80, 100, 
125*, 150*, 175*, 203* atmospheres (excess above one atmosphere). 

/. Broadening: 

Within the region X 4000 to X 4600 : 

1. All lines are broader under high pressures than under atmospheric pressure. 

2. The broadening increases with the pressure ; it has not been determined whether 

the increase is continuous and linear with the pressure. 

3. The broadening of all lines is uusymmetrical, being greater on the red side. 

4. The amount of broadening is different for different lines. 

5. Two types of broadening have been observed : some lines at first become faint 

and hazy, almost resembling bands which are completely dissipated under high 
pressures (series lines) ; others, though much broadened, remain well-defined 
lines (non-series lines). 

6. No simple relation has been found between the width of a line under pressure 

and its original intensity. 

7. The intensity curves of the sharp lines under pressure are steeper towards the 

violet than are those of the nebulous lines. The sharp and nebulous lines 
retain their characteristic hard and soft appearances at all pressures. 

8. The nebulous and sharp non-series lines broaden to about the same extent for 

the well-defined lines, the width may be as great as 12 A.U. at 203 
atmospheres.* 

9. The broadening at first appears to increase more rapidly than the displacement 

at first, making measurements at low pressures less accurate than those at 
high pressures. 

//. Displacement : 

Within the region X 4000 to X 4600 : 

1. Under pressure the most intense portion of every line is displaced from the 

position it occupies at a pressure of 1 atmosphere. 

2. The displacement is in the direction of greater wave-length. 

3. The displacement is real and not due to unsymmetrical broadening, i.e., the line 

is broadened about a displaced position. 

4. The displacement of each line is, within the limits of accuracy of the experiments^ 

continuous and linear with the pressure. 

5. The rates of increase of the displacement with the pressure are different for 

different lines. 

* Added October 19, 1908. G. D. 
VOL. CCIX. A. 2 G 



226 ON THE EFFECT OF PRESSURE UPON ARC SPECTRA. 

6. The lines belonging to the first and second subordinate series have greater 

displacements than the non-series lines. Their great width precludes accurate 
measurement. 

7. The displacements of non-series lines are functions of their wave-lengths. The 

evidence indicates that they vary with a power of the latter at least as great 
as the third and possibly as great as the sixth. 

8. There is some reason to believe that there are two values for the displacement ot 

a line at one and the same pressure. 

9. The mean displacement of the non-series lines is 12'2 thousandths of an 

Angstrom unit per atmosphere. The largest displacement measured is a little 
more than 2 A.U. at 203 atmospheres.* 

777. Reversals: 

None of the copper lines within this region showed any signs of reversal under 
pressure. 

IV. Relative Intensities: 

Within the region X 4000 to X 4600 : 

1. Changes in relative intensities of lines occur under pressure. 

2. Those belonging to either the first or second subordinate series vanish at about 

70 atmospheres and do not reappear as the pressure is increased. 

3. Members of the first sub-series become at low pressures faint and hazy, almost 

resembling bands, and are, at high pressures, dissipated. There is, however, 
always a marked cloudiness in the neighbourhood of their original positions. 

4. Members of the second sub-series gradually diminish in intensity without 

abnormal widening. No cloudiness is distinguishable near their original 
positions. 

5. Of the non-series lines those that are nebulous are strengthened relatively to 

those that are sharp. 

6. Lines strengthened under pressure do not correspond with those given by other 

workers as " enhanced " lines. 

V. Brightness: 

The brightness of the copper arc increases enormously with the pressure of the 
surrounding air. 

I take this opportunity of thanking Dr. SCHUSTER for his advice and continued 
interest in this work, which was undertaken at his suggestion, and I also thank 
Prof. EUTHERFORD for having placed the necessary apparatus at my disposal. 
Mr. R. Rossi, B.Sc., and Mr. W. C. LANTSBERRY rendered valuable assistance in the 
high-pressure work, which I have pleasure in acknowledging. 

* Added October 19, 1908. 



Dr. W. Geoffrey Dujfield. 



Phil. Tram., A, rol. 209, Plate 10. 



PJ 



O O5 
00 <N < 



oo 
I- 



? 
M n 




Dr. I!'. Geoffrey J)nffidd. 



1'liil. J/vm.s., .1, rot. 20!), Plate 11. 



+ 5 



15 



70 



+ 80 



Sfc 



St 



Oblit 



St 
2nd Bub-series- 



Oblit 



St 



Weiikeiied linns lire marked \V"k ; strc-ngthened lines are marked St ; obliterated lines arc marked Oblit. 



[ 227 ' 



X. Results of Magnetic Observations at Stations on the Coasts of the British 

Isles, 1907. 

By Commander L. W. P. CHETWYND, R.N., Superintendent of Compasses. 

Communicated by Rear-Admiral A. M. FIELD, F.Ii.S. 

Received July 14, Read December 10, 1908. 

1. WITH a view to comparing the values of Secular Change of Declination, Horizontal 
Force and Dip, at various stations on the coasts of the British Isles, with the values 
derived from the continuous records at Kew Observatory, the Hydrographer (Rear- 
Admiral A. MOSTYN FIELD, F.R.S.) directed that during the year 1907 observations 
were to be made at certain stations, selected from those which had been occupied 
by Prof. RtiCKER and Dr. THORPE during their Magnetic Survey* for the epoch 
1st January, 1891. 

2. The observers detailed for the work were Captain M. H. SMYTH, R.N., 
H.M.S. "Research"; Captain W. PUDSEY-DAWSOX, R.N., H.M.S. "Triton"; and 
Captain J. W. COMBE, R.N., H.M. Surveying Vessel " Gladiator." 

(The observers' names are subsequently indicated by their initials.) 

The instruments with which they were supplied were : 

M. H. S 

W. P.-D 

J. W. C. 



Unifilar. 


Dip circle. 


1G1 


186 


60 


188 


25 


27 



3. Careful reference, kindly verified by Dr. THORPE, was made to ensure the exact 
observation spot at each station being re-occupied. 

4. To reduce all results to a common instrumental standard, observations were 
made at Kew, before the commencement of the field observations and after their 
completion, and the results of comparing the values obtained by each instrument with 
the values derived from the magnetograms were applied as corrections for instrumental 
differences, thus reducing the field observations to the Kew Instrumental Standard. 

The corrections so applied are given in Table I. 

* 'Phil. Trans.,' A, vol. 188 (1896). 
VOL. CCIX. A 450. 2 G 2 25.1.09 



228 COMMANDER L. W. P. CHETWYND: EESULTS OF MAGNETIC OBSERVATIONS 



TABLE I. Corrections for Instrumental Differences. 



Horizontal Force. 


Unifilar No. 


161. 


Unifilar No. GO. 


Unifilar No. 25. 


Magnet 25A. Magnet 25o. 


+ 3 7 


-ly 


+ 4y +16y 


Declination. 


Unifiliir No. 161. 


Unifilar No. GO. 


Unifilar No. 25. 


-0 


'4 




-0'-2 


+ !'! 


Inclination. 


Dip circle No. 186. 


Dip circle No. 188. 


Dip circle No. 27. 


Needle 1. 


Needle 2. 


Needle 1. 


Needle 2. 


Needle 1. Needle 2. 


+ 0'-91 


+ 1' 


14 


-0'-4 


+ 0'-56 


-l'-51 -l'-26 



5. To reduce the observed values to a common epoch, the field observations were 
compared with synchronous values derived from the Kew magnetograms, and the 
differences as recorded at Kew between these latter values and the mean value for 
1906 and 1907 were applied as a correction to the values at the field stations to 
reduce them to the epoch 1st January, 1907. 

The comparisons were made by the Staff of the Observatory Department of the 
National Physical Laboratory and the resulting differences supplied by Dr. CHREE, 
F.E.S. 

6. A summary of the results of all the field observations is given in the following 
Table II. : 



AT STATIONS ON THE COASTS OF THE BRITISH ISLES, 1907. 



229 



TABLE II. Summary of Results. 



Place. 


Date. 


Declination W. 


Horizontal Force. 


Inclination. 


Vertical 
force. 




Reduced 




Reduced 




Reduced 


Reduced 






Observed. 


to 1st 
January, 
1907. 


Observed. 


to 1st 
January, 
1907. 


Observed. 


to 1st 
January, 
1907. 


to 1st 
January 
1907. 




1907 


, 


, 






/ 


/ 




Harwich .... 
Great Grimsby. 
Sunderland. . . 
Stonehaven . . 
Kirkwall .... 
Dublin 


8-9 May . . 
13-14 . . 
17 
21-22 . . 
4-6 June . . 
9-10 May . . 
8-9 October 


15 32-3 
16 35-8 
17 29-2 
18 20-4 
19 7-7 
19 47-3 
20 39-3 


15 31-8 
16 32-2 
17 29-7 
18 20-3 
19 10-3 
19 47-0 
20 38-3 


0-18409 
0-17627 
0-17086 
0-16345 
0-15445 
0-17560 
0-15343 


0-18419 
0-17640 
0-17093 
0-16365 
0-15445 
0-17550 
0-15361 


67 5-5 
68 23-4 
69 14-7 
70 27 -G 
71 48-8 
68 30-3 
71 49-5 


67 6-9 
68 24-3 
69 15-3 
70 27-4 
71 49-1 
68 32-4 
71 50-2 


0-43636 
0-44565 

0-45128 
0-46103 
0-47027 
0-44645 
0-46822 


Tanora Mor*. . 


Weymouth. . . 
Milford Haven . 
Stranraer. . . . 


15-16 April. . 
13-16 . . 
12-17 June. . 


16 55-6 
18 6-2 
19 31-3 


16 51-5 
18 8-9 
19 34 '8 


0-18774 

0-18187 
0-16811 


0-18790 
0' 18221 
0-16844 


66 32-8 
67 38-6 
69 43-4 


66 31-5 
67 36-6 
69 41-7 


0-43266 
0-44229 
0-45523 


Letterkenny . . 
Loch Melfort. . 


19-22 July . . 
23-26 . . 


20 56-4 
19 47-4 


20 59-3 
19 50-9 


0-16689 
0-16523 


0-16713 
0-16553 


70 0-4 
70 13-5 


69 59-4 
70 11-7 


45788 
0-45965 



7. In the subjoined abstract of results the plan adopted by RUCKER and THORPE 
in their memoirs has been followed, and in each case the data given are as follows : 

1. The number and name of the station ; 

2. The initials of the observer ; 

3. The distinguishing numbers of the instruments used ; 

4. The date ; 

5. The latitude and longitude of the station ; 

6. Angles, magnetic bearings, or other information for fixing the position. 

For each element is given : 

1. The date ; 

2. The Greenwich mean time of observation ; 

3. The observed value with all corrections applied (8, H, and 9} ; 

4. The value reduced to the epoch 1st January, 1907 (8 > H , and ) ; 

5. The means respectively of 3 and 4. 

For convenience in reference the numbers assigned to the stations by RUCKER and 
THORPE have been retained. 



Sec footnote, p. 236. 



230 COMMANDER L. W. P. CHETWYND: RESULTS OF MAGNETIC OBSERVATIONS 



421. HARWICH. W. P.-D. (60, 188.) 8-9 May, 1907. 

Latitude 51 56' 36" N., Longitude 1 17' 11" E. 

On reclaimed land west of the town. 

o I II 

Martello Tower, Shotley 36000 

Water Tower 16 12 

Grand Hotel (Flagstaff) 5950 

St. Nicholas Church Spire 93 32 

Low Chimney, Cement Works 250 55 

High ' 26020 

Chimney, Ramsay Island 304 13 

(True bearing of Chimney, Ramsay Island, N. 67 56' 42" W.) 

Declination, 

Date. G.M.T. S. 

h. m. 

8 May 1157a.m. 1533'9 1531-7 

8 3 34 p.m. 15 32-3 15 32-1 

9 10 21a.m. 15 31-3 15 32-7 

9 2 41 p.m. 15 32-9 15 31 '0 

9 4 17 15 31-3 15 31-4 

Means ... 15 32'3 15 31-8 

Horizontal Force. 

Date. G.M.T. H. H . 

li. m. 

8 May 1047a.m. 0-18398 0-18415 

8 , 241p.m. 0-18418 0-18415 

9 , 924a.m. G'18406 0-18426 

9 , 1 27p.m. 0-18415 0-18420 



Means 



0-18409 



0-18419 



Inclination. 



Date. 



G.M.T. 



e. 



8 May 
8 . 
9 



h. m. 

1 17 p.m. 
4 49 
11 47 a.m. 

Means 



67 5-3 
67 5-2 
67 6-1 

67 5-5 



67 6-7 
67 6-7 

67 7-2 

67 6-9 



AT STATIONS ON THE COASTS OF THE BRITISH ISLES, 1907. 



231 



406. GEEAT GEIMSBY. W. P.-D. (60, 188.) 13-14 May, 1907. 
Latitude 53 33' 14" N., Longitude 5' 24" W. 

In a pasture field, almost in a line with the fence of Nunsfield Grounds and 40 feet 
from the brook. 

A guide post on the main road is seen just to the right of a gate post. 

Declination. 



Date. 


G.M.T. 


8. 


So. 


13 May 
13 
13 
14 


h. m. 

10 59 a.m. 
2 52 p.m. 
4 42 
7 52 a.m. 


o / 

16 34-0 
16 34-1 
16.36-0 

16 28-9 


16 30-2 
16 29-7 
16 34-0 
16 34-7 


Means . . . 


16 35-8 


16 32-2 



Horizontal Force. 



Date. 


G.M.T. 


H. 


H . 


13 May . . . 
13 
13 


h. m. 
10 13 a.m. 
1 53 p.m. 
3 54 


0-17613 
0-17630 
0-17638 


0-17650 
0-17637 
6-17634 


Means . . . 


0-17627 


0-17640 



Inclination. 



Date. 


G.M.T. 


e. 


00. 


13 May . 
U ... 


h. m. 
25 p.m. 
9 8 a.m. 


/ 

68 22-7 
68 24-0 


68 24-5 
68 24-0 


Means . . . 


68 23-4 


68 24-3 



232 COMMANDER L. W. P. CHETWYND: RESULTS OF MAGNETIC OBSERVATIONS . 



633. SUNDEKLAND. W. P.-D. (60, 188.) 17 May, 1907. 
Latitude 54 53' 30" N., Longitude 1 24' 23" W. 

In a pasture field, north of Humbledon Hill, close to a fence, and 60 yards to the 
northward from the main road. 

Declination. 



Date. 


G.M.T. 


8. 


So- 


17 May . 
17 
17 
17 


ll. in. 

9 47 a.m. 
11 54 
3 31 p.m. 
5 11 


o / 

17 29-9 
17 28-9 
17 29-9 
17 28 ! 


17 32-8 
17 28-5 
17 28-6 
17 29-0 


Means . . . 


17 29-2 


17 29-7 



Horizontal Force. 



Date. 


G.M.T. 


H. 


H. 


17 May 
17 
17 


h. in. 

8 46 a.m. 
1 G p.m. 
4 30 


0-17074 
0-17080 
0-17103 


0-17094 
0-17090 
0-17094 


Means . . . 


0-17086 


0-17093 



Inclination. 



Date. 


G.M.T. 


0. 


00- 


17 May ..... 
17 


h. in. 

11 6 a.m. 
2 39 pm 


O / 

69 14-9 
69 14-5 


O 1 

69 15-2 
69 15-4 












Means . 


69 14-7 


69 15-3 



AT STATIONS ON THE COASTS OF THE BRITISH ISLES, 1907. 



233 



217. STONEHAVEN. W. P.-D. (60, 188.) 21-22 May, 1907. 

Latitude 56 58' 1" N., Longitude 2 14' 10" W. 
In a field, close to the fence of Farochie and north of Camp Hill. 

Declination. 



Date. 


G.M.T. 


S. 



S . 


21 May 


li. m. 

10 37 a.m. 


o / 

18 16-9 


/ 

18 20-1 


21 
21 
22 
22 


2 12 p.m. 
4 25 
11 7a.m. 
1 7 p.m. 


18 19-2 
18 20-2 
18 20-9 
18 24-9 


18 18-2 
18 20-0 
18 21-1 
18 21-9 




Means . . . 


18 20-4 


18 20-3 



Horizontal Force. 



Date. 


G.M.T. 


H. 


H . 


21 May 


h. m. 

9 53 am 


0-16347 


0-16366 


21 
22 
22 . 


1 21 p.m. 
10 16 a.m. 
2 2 p.m. 


0-16341 
0-16343 
0-16348 


0-16361 
0-16366 
0-16366 












Means . . . 


0-16345 


0-16365 



Inclination. 



Date. 


G.M.T. 


ft 


00. 


21 May 


h. m. 
11 52 a.m. 


70 28-7 


O 1 

70 28-4 


21 


3 39 p m 


70 26-4 


70 26-4 












Means . . . 


70 27-6 


70 27-4 



VOL. CCIX. A. 



2 H 



234 COMMANDEE L. W. P. CHETWYND: RESULTS OF MAGNETIC OBSERVATIONS 



139. KIRKWALL. W. P.-D. (60, 188.) 4-6 June, 1907. 
Latitude 58 59' 17" N., Longitude 2 57' 8" W. 

Twenty feet from the road by Cromwell's Fort, 33 yards from the Coastguards' 
v/all along the road. 

Declination. 



e 








Date. 


G.M.T. 


8. 


So- 




h. m. 


, 


o / 


4 June 


1 1 2 a.m. 


19 7-7 


19 9-9 


4 


1 56 p.m. 


19 8-2 


19 8-4 


4 


57,, 


19 6-6 


19 8-6 


6 


9 9 a.m. 


19 5-7 


19 11-9 


6 


10 50 


19 10-1 


19 12-7 




Means . . . 


19 7-7 


19 10-3 



Horizontal Force. 



Date. 


G.M.T. 


H. 


Ho. 


4 June 
4 


h. m. 
10 10 a.m. 
2 47 p.m. 


0-15430 
0-15475 


0-15445 
0-15462 


6 


9 53 a.m. 


0-15431 


0-15427 












Means . . . 


0-15445 


0-15445 



Inclination. 



Date. 


G.M.T. 


e. 


00- 


4 June 
4 


h. m. 
11 p.m. 
4 20 


o t 

71 50-9 
71 46-7 


o / 

71 49-5 
71 48-6 












Means . . . 


71 48-8 


71 49-1 



AT STATIONS ON THE COASTS OF THE BRITISH ISLES, 1907. 



235 



768. DUBLIN. M. H. S. (161, 186.) 9-10 May, 1907. 
Latitude 53 20' 35" N., Longitude 6 15' 21" W. 

In the grounds of Trinity College, on the eastern side of the path, 65 feet from the 
edge and 46'25 feet north of the north side'of the small building (marked Observatory 
on the ordnance map), now used as a tool shed. 

Note. Captain M. H. SMYTH observes that " the observations at Trinity College, 
Dublin, are not very reliable, owing to the proximity of electric tramlines which 
surround the College grounds, and that this station cannot be looked upon as suitable 
for the purpose of determining magnetic elements in future." 

Declination. 



Date. 


G.M.T. 


8. 


So. 


9 May . 


h. m. 
431pm 


f 

19 '44-5 


o / 

19 44-0 


10 


951 


19 53-4 


19 51-3 


10 


5 15 


19 43-9 


19 45-G 












Means . . . 


19 47-3 


19 47-0 



Horizontal Force. 



Inclination. 



Date. 


G.M.T. 


H. 


H . 


9 May 


h. m. 

4 40 p.m. 


0-17557 


0-17543 


10 


2 43 


0-17562 


0-17556 




Means . . . 


0-17560 


0-17550 



Date. 


G.M.T. 


e. 


00- 


9 May 


h. m. 
1 15 p.m. 


68 30-5 


/ 

68 32-5 


10 


11 17 a.m. 


68 30-1 


68 32-3 












Means . . . 


68 30-3 


68 32-4 



2 H 2 



236 COMMANDER L. W. P. CHETWYND: RESULTS OF MAGNETIC OBSERVATIONS 



226. TANERA MOR.* M. H. S. (161, 186.) 8-9 October, 1907. 

Latitude 58 0' 36" N., Longitude 5 24' 9" W. 

On the steep slope immediately south of the old fish-curing establishment, with the 
right tangent of the wall 126 feet distant bearing N. 6 26' 30" E. (true). Corner of 
wall surrounding cultivated ground 63 feet distant bearing S. 86 1' 30" W. (true). 
Fixed mark (a cairn of stones on Rudha' Ard-na-goine) bearing N. 24 7' 30" E. (true), 
distant approximately 1022 yards. 

Declination. 



Date. 


G.M.T. 


5. 


So- 


8 October ..... 


h. in. 

.35 p.m. 


o / 

20 40-9 


o / 

20 39-9 


8 


1 28 


20 40-5 


20 38-2 


8 


2 48 


20 40-6 


20 39-1 


9 


3 7 


20 35-3 


20 35-8 












Means . 


20 39-3 


20 38-3 



Horizontal Force. 



Date. 


G.M.T. 


H. 


Ho. 


8 October 


h. m. 
4 1 2 p.m 


0-15362 


0-15370 


9 


1 36 


0-15323 


0-15351 












Means . . . 


0-15343 


0-15361 



Inclination. 



Date. 


G.M.T. 


6. 


00- 


8 October 


h. ra. 
10 26 a.m. 


/ 

71 49-8 


/ 

71 50-7 


9 


10 35 


71 49-1 


71 49-6 












Means . . . 


71 49-5 


71 50-2 



* This station being in a region of disturbance, the results should be treated with caution. 



AT STATIONS ON THE COASTS OF THE 'BEITISH ISLES, 1907. 



237 



674. WEYMOUTH. M. H. S. (161, 180.) 15-16 April, 1907. 
Latitude 50 36' 19" N., Longitude 2 26' 44" W. 

To the south of the Nothe, close to high line ; a brick is buried just under the 
surface. 

True bearings from the observation spot : 



Breakwater Light House Vane 

Centre of beacon on breakwater 

Left tangent of Naval Torpedo Range House . . 

Tower of Bincleave House S. 39 19 50 W. 

Flagstaff of coastguard lookout-house on Nothe . . . N. 6 25 20 E. 



S. 43 3 40 E. 
S. 36 24 40 E. 

S. 15 40 E. 



Flagstaff on south bastion of Not! ie Fort . . . 
Right tangent of sea wall. South side of Nothe . 
Left tangent of breakwater outside the, Fort . . 
Left tangent of northern arm of breakwater . . 

Declination. 



N. 58 24 20 E. 

N. 72 59 20 E. 

S. 45 37 25 E. 

S. 44 36 25 E. 



Date. 


G.M.T. 


S. 


So. 


15 April 


h. m. 
2 40 p ni 


16 54"> 


/ 

16 51-9 


16 


27 


16 55 '9 


16 5' 1 


16 


2 38 


16 56-6 


16 50-5 












Means . . . 


16 55-6 


16 51-5 



Horizontal Force. 



Date. 


G.M.T. 


H. 


H . 


15 April 


h. m. 
49 p.m. 
2 50 


0-18767 
0-18781 


0-18788 
0-18792 


16 




Means . . . 


0-18774 


0-18790 


Inclination. 


Date. 


G.M.T. 


ft 


00- 


15 April 


h. m. 

4 33 p.m. 
9 31 a.m. 


66 31-6 
66 34-0 


o / 

66 32-5 
66 30-5 


16 




Means . . . 


66 32-8 


66 31-5 



238 COMMANDER L. W. P. CHETWYND: RESULTS OF MAGNETIC OBSERVATIONS 



527. MILFORD (NEW MILFORD). ' J. W. C. (25, 27.) 13-16 April, 1907. 
Latitude 54 42' 26" N., Longitude 4 56' 48" W. 

In a field belonging to Mr. Carron, situated to N.W. of an iron church now built 
close to the site of the previous observation spot of 1887-1892, 174 feet N.W. from 
the main road and 160 feet N.E. from a post near the tennis ground. 

Declination. 



Horizontal Force. 



Date. 


G.M.T. 


5. 


So- 


13 April 


h. ni. 
414 p.m. 


o / 

18 5-5 


/ 

18 7-7 


15 
16 
16 


4 .W 

8 3 ;i.m. 

9 28 


18 8-6 
18 0-4 
18 2-2 


18 10-7 
18 7-4 
18 6-5 


16 


4 p.m. 


18 14-3 


18 12-2 












Means . . . 


18 6-2 


18 8-9 



Date. 


G.M.T. 


H. 


H . 


13 April 


li. in. 
1 p.m. 


0-18212 


0-18221 (Magnet 25A) 


15 


1 5 


0-18187 


0- 18220 ( 25D) 


15 


1 37 


0-18197 


0- 18216 ( 25A) 


15 
15 . . 


15 
45 


0-18177 
0-18160 


0- 18248 ( 25c) 
0- 18201 ( 25A) 












Means . 


0-18187 


0-18221 



Inclination. 



Date. 


G.M.T. 


e. 


00- 


13 April 


h. in. 

3 p.m. 


O 1 

67 35-2 


O / 

67 35-3 


15 


11 58 a.m. 


67 42-6 


67 40-4 


15 
16 ... 


3 29 p.m. 
10 58 a.m. 


67 40-2 
67 38-9 


67 38-6 
67 34-1 


16 


2 35 p.m. 


67 35-9 


67 34-6 












Means . . . 


67 38-6 


67 36-6 



AT STATIONS ON THE COASTS OF THE BRITISH ISLES, 1907. 



239 



220. STRANBAEU. J. W. C. (25, 27.) 12-17 June, 1907. 

Latitude 54 54' 25" N., Longitude 5 2' 10" W. 
In a field, 300 yards N. W. by W. of Schuchan Church. 

Declination. 



Date. 


G.M.T. 


S. 


So. 




h. m. 


O / 


3 / 


12 June 


4 48 p.m. 


19 35-2 


19 34-1 


13 


9 22 a.m. 


19 24-3 


19 32-3 


13 


3 57 p.m. 


19 40-1 


19 36-1 


14 


8 59 a.m. 


19 25-7 


19 34-2 


15 


9 30 


19 24-0 


19 33-0 


17 


4 20 p.m. 


19 38-2 


19 38-8 




Means . 


19 31-3 


19 34-8 



Horizontal Force. 



Date. 


G.M.T. 


H. 


Ho. 


13 June 


h. m. 
16 p.m 


0-16807 


0-16835 (Magnet 25A) 


13 


52 


0-16805 


0-16838 ( , 25o) 


14 , 


11 15 a.m. 


0-16801 


0- 16846 ( 25D) 


14 


11 43 


0-16829 


0- 16855 ( 25A) 




Means . 


0-16811 


0-16844 



Inclination. 



Date. 


G.M.T. 


e. 


00. 


12 June 


h. m. 

3 9 p.m. 


O / 

69 41-9 


o / 

69 41-7 


13 


11 10 a.m. 


69 45-5 


69 42-7 


13 
14 


3 9 p.m. 
10 2 a.m. 


69 42-0 
69 44-1 


69 41-2 
69 41-2 












Means . . . 


69 43-4 


69 41-7 



240 COMMANDER L. W. P. CHETWYND: RESULTS OF MAGNETIC OBSERVATIONS 



816. LETTERKENNY. J. W. C. (25, 27.) 19-22 July, 1907. 
Latitude 54 56' 55" N., Longitude 7 43' 55" W. 

In a meadow on the east side of the town, about 300 yards from the main street 
and 15 yards east of a lane running down to the river. 
The spire of the church in the town bore N. 25 W. 

Declination. 



Date. 


G.M.T. 


8. 


So- 


19 July 
20 , 


h. in. 
4 40 p.m. 
10 1 a.m. 


O / 

21 0-5 
20 54-6 


o / 

20 56-4 
20 58-9 


20 , 

21 , 
21 , 


4 30 p.m. 
9 59 a.m. 
4 59 p.m. 


20 57-1 
20 55-0 
20 58-0 


20 57-5 
21 2-4 
21 0-0 


22 , 


9 59 a.m. 


20 53-4 


21 0-5 




Means . 


20 56-4 


20 59-3 



Horizontal Force. 



Date. 


G.M.T. 


H. 


H . 


19 July 
19 


li. in. 

2 3 p.m. 
2 1 


0-16680 
0-16701 


0-16715 (Magnet 25D) 
0- 16720 ( 25A) 


20 
20 


1 20 

1 56 


0-16680 
0-16696 


0- 16709 ( 25o) 
0- 16706 ( 25A) 




Means . . . 


0-16689 


0-16713 



Inclination. 



Date. 


G.M.T. 


e. 


00- 


19 July . 


h. m. 
3 48 pm 


O / 

70 0-3 


/ 

69 59-3 


20 
20 


11 29 a.m. 
3 43 p.m. 


70 0-7 
70 0-1 


69 59-1 
69 59-7 




Means . 


70 0-4 


69 59-4 



AT STATIONS ON THE COASTS OF THE BRITISH ISLES, 1907. 



241 



155. LOCH MELFORT. J. W. C. (25, 27.) 23-26 July, 1907. 

Latitude 56 16' 7" N., Longitude 5 30' 32" W. 
On the west side of Fearnach Bay, close to the shore. 

Declination. 



Date. 


G.M.T. 


8. 


So. 


23 July 
24 


ii. in. 
4 50 p.m. 
8 59 a.m. 


o / 

19 46-0 
19 48-4 


19 47-6 
19 54-5 


24 , 
24 , 


9 45 
4 14 p.m. 


19 47-7 
19 48-4 


19 52-2 
19 49-8 


24 


4 42 


19 48-4 


19 50-1 


25 , 

25 , 
26 


9 44 a.m. 
4 44 p.m. 
9 a.m. 


19 44-1 
19 50-7 
19 45-4 


19 51-4 
19 49-1 
19 52-G 












Means . 


19 47-4 


19 50-9 



Horizontal Force. 



Date. 


G.M.T. 


11. 


Ho. 






] i . in . 








24 July 


35 p. Til 


0-16511 


0-16543 (Mao-net 


25n) 


24 , 


1 9 


0-16552 


0- 16567 ( . 


25A) 


25 , 


56 


0-16531 


0- 16562 ( , 


25] >) 


25 , 


1 29 


0-16546 


0- 16553 ( 


25A) 


26 , 


10 2 a.m. 


0-16507 


0- 16545 ( 


25 A) 


26 , 


10 29 


0-16489 


0- 16546 ( , 


25n) 




Means . 


0-16523 


0-16553 





Inclination. 



Date. 


G.M.T. 


e. 


0o. 


24 July 
24' 


ll. 111. 

11 6 a.m. 
3 4 p.m. 


70 15-2 
70 13-4 


70 12-8 
70 11-6 


25 ,; 

25 


10 46 a.m. 
3 16 p.m. 


70 14-1 
70 11-1 


70 10-7 
70 11-5 




Means . . . 


70 13-5 


70 11-7 



VOL. CCIX. A. 



2 I 



242 COMMANDER L. W. P. CHETWYND: RESULTS OF MAGNETIC OBSERVATIONS 

8. Comparing the values deduced for the epoch 1st January, 1907, with the 
corresponding values for 1st January, 1886, or 1st January, 1891 (the epochs of 
RtiCKER and THORPE'S survey), the resulting mean annual changes at each station are 
as shown in columns 2, 5, 8, and 11 of Tahle III., in which the stations are arranged 
according to their latitude. 

9. For comparison, in the same table are given (columns 3, 6, 9, and 12) the mean 
annual changes at Kew, the differences of mean annual change between Kew and the 
Field stations being shown in columns 4, 7, 10, and 13. 

10. The resulting comparison shows that the mean annual change of Declination is 
generally greater at the Field stations than at Kew. The mean change at Kirkwall 
is l'-5 greater than at Kew, but the results do not indicate a very marked gradual 
increase with increase of latitude. 

11. The mean .annual change of Horizontal Force appears to be less at the Field 
stations than at Kew, the differences being greater in the northern latitudes. 

12. The mean annual change of Inclination is less at the Field stations than at 
Kew, the difference being greater in the northern latitudes. 

13. The mean annual change of Vertical Force during the sixteen-year period 
1891 to 1907 is less at the Field stations than at Kew, and, with the exceptions of 
Dublin and Tanera Mor, the Field station results are remarkably similar. 

14. The value of the Declination at Kew for the year 1886, as originally recorded, 
was 18 18 /- 5, derived from absolute observations only. 

Compared with the value for the year 1 907, derived from quiet-day magnetograms, 
this gives a mean annual change, during the 21 years' interval, of 5''.3. 

The corresponding values at Greenwich and Stonyhurst are respectively 5''5 and 
5 /- 6. The mean from the results of those Field stations at which the 21 years' 
interval is available is 5 / 7, but in the latter case the comparison is from 1886 
to 1907 . 

15. The originally recorded value at Kew lias, Dr. CHREE informs me, been 
amended. 

Previous to the year 1890 Kew had no fully corrected declination curves, but in 
1892 a table of mean annual values was compiled based on the absolute observations 
corrected for diurnal inequality by means of statistics derived from the diurnal 
inequalities for short series of years ; these corrections unquestionably improve 
the value derived from absolute observations alone, and the resulting value for the 
epoch 1st January, 1886, is 18 15 /- 3; this latter value has been used in calculating 
the mean change at Kew 1886 to 1907 , resulting in the value 5''2, as given in 
Table III. 

16. Comparing this value at Kew with corresponding values at those Field stations 
at which the same 21 years' interval is available, viz., Weymouth, Harwich, Dublin, 
Milford, Stranraer, and Kirkwall, the mean of the values at these stations is 0''5 
greater than at Kew. 



AT STATIONS ON THE COASTS OF THE BEITISH ISLES, 1907. 243 

17. The mean annual change at Kew during the 16-year period, 1891 to 1907 , is 
4 /- 9. Comparing this with the values at those stations at which the 16 -years' interval 
is available, viz., Great Grimsby, Milford, Suriderland, Letterkenny, Loch Melfort, 
Stonehaven, and Tanera Mor, the mean of the values at the Field stations is /- 2 
greater than at Kew. 

At Milford, where results are available for both the 21- and the 16-year periods, 
the mean for the former is 0' - 5 greater than Kew, and for the 16-year period is the 
same as Kew. 

18. These results seem to indicate that the reduction in the amount of the annual 
change has been greater at the Field stations than at Kew. 

19. This is corroborated by a comparison (p. 244) of the Declination-change curves 
for Kew and Stonylmrst (fig. I). 

20. Comparison of Mean Annual Chanc/e of Declination at Kew, Greenwich, 

and Stonyhurst. 

To compare the annual change at Kew, Greenwich, and Stonyhurst, the mean of 
five successive yearly differences of Declination is assigned as the mean annual change 
for the mid-year of the 5-year period. 

Thus the mean of the yearly differences from 188G. to 1891.,-, is assigned as the 
mean annual change for the year 1889. The mean annual value representing the 
value for the middle of the year, the quinquennial mean change is allotted to 
1st January of the middle year. 

21. Curves of which these quinquennial mean values are the ordinates have been 
drawn, as shown in fig. 1. 

22. The comparison of these curves indicates that between the years 1886 and 1894 
(embracing the period of HUCKER, and THORPE'S survey) the value of the secular 
change at Stonyhurst Avas considerably in excess of that at Ke\v this being in 
agreement with the results found by RUCKER and THORPE that the value was greater 
in the North-west than at Kew. 

Since the year 1894 the values at Stonyhurst and Kew are in closer agreement and 
that at Stonyhurst slightly less than at Kew. 

23. Figs. 2, 3, and 4 show respectively the curves of annual change of Declination, 
Horizontal Force, and Inclination at Kew derived from quinquennial means. 

24. The Declination-change curve, fig. 2, indicates that the annual change which 
was decreasing in amount from the epoch 1893 to 1904 is now increasing in amount, 
and that the mean value at the present epoch (l January, 1907) is 4''8. 

25. Assuming the mean difference between Kew and the rest of the British Isles, 
derived from observations at 16 years' interval, to be as given (see paragraph 17), 
the mean value of the change for the United Kingdom is 5'. 

26. The Horizontal Force-change curve, fig. 3, indicates that the amount of annual 

2 I 2 



244 COMMANDER L. W. P. CHETWYND: RESULTS OF MAGNETIC OBSERVATIONS 

increase has, since the year 1898, been diminishing, that this annual increase is at 
present very small, and may shortly become an annual decrease. Thus, if AH 
represent the difference of the values of Horizontal Force for successive years, AH has 
been positive, but has since the year 1898 diminished in numerical value. 

AH is at present very small and may shortly change from being + to being . 

27. The Inclination-change curve, fig. 4, indicates that the amount of the annual 
decrease has been, and still is, diminishing, and that its present value is 1'. Thus, 
if A0 represents the difference of the values of Inclination for successive years, A0 has 
been, and still is, negative, but has diminished in numerical value until it is now 1'. 




. , . _j i 1 i ; i 1 > - 

1889 .10 91 sa 93 94 93 96 37 S3 99 I900 Ol 0! (X5 04 K> 06 07 08 

Fig. 1. Curves of mean annual decrease of Declination at Ke\v, Greenwich, and Stonyhurst 

(derived from quinquennial means). 



1889 90 91 9 93 9* 95 86 97 98 99 1900 01 OZ 03 04 05 

Fig. 2. Curve of mean annual decrease of Declination at Kew 
(derived from quinquennial means). 



06 07 



03 



AT STATIONS ON THE COASTS OF THE BRITISH ISLES, 1907. 



245 



Tearf^ifff 
only. 



lOy 



1889 90 91 HI 93 94 95 96 97 is S9 1300 01 02 03 0* 05 06 07 "08 



Fit;. ''. Curve of mean annual increase of Horizontal Force ;it Kew 

O 

(derived from quinquennial means). 




Fig. 4. Curve of mean annual decrease of Inclination at Kew 
(derived from quinquennial means). 

Comparison of Declination Value* Observed at tivit tvit/t tlivse on Shore. 

To compare the values of Declination at sea with those observed on shore, 
H.M. ships "Research" (Captain M. H. SMYTH, R.N.) and "Triton" (Captain 
W. PUDSEY-DAWSON, RN.) were instructed to obtain the values of the Declination 
by "swinging ship" in deep water in the vicinity of the shore stations. 

The vessels were swung turning to starboard and to port and a mean of the results 
accepted as the value of the Declination. 

These results have not been corrected for diurnal variation, but allowance has been 
made for secular change to reduce them to epoch 1st January, 1907. 

An allowance in each case has been made for the difference of position from shore 
station, such allowance having been derived from a consideration of the values shown 
by the mean lines of equal Declination on the Admiralty charts of equal Declination. 

The results, which cannot be considered to a closer degree of accuracy than 10', 
are given in Table IV. 



246 COMMANDER L. W. P. CHETWYND: RESULTS OF MAGNETIC OBSERVATIONS 

The comparison with the values deduced from observations at the nearest shore 
station is given in Table V. 

The main feature which this comparison brings out is that the sea values on the 
East Coast come out generally greater, and on the West Coast generally less, than 
the corresponding value deduced from observations on shore. 

The differences appear to be slightly greater in the Northern latitudes. 

It is intended to investigate further the source of this difference. Meantime, for 
navigational purposes, the values as found at sea have been accepted, and they are, 
in so far as the English Channel is concerned, corroborated by results from other 
vessels. 

The original records of the observations here discussed, as well as charts showing 
the exact positions of the shore stations, are retained in the Compass Branch of the 
Hydrographic Department of the Admiralty. 



AT STATIONS ON THE COASTS OF THE BRITISH ISLES, 1907. 



&JD 

s 

43 

O 



o 

0) 






PH 

i 

o 



- 

H5 

FQ 



3i~ 

03 O 





S Ii 

C 9 



5, 



3J 



a 

c 






52 



r-< O> O 51 CC 

. -"- 1 
11 + 11 



CV GO OS 30 O5 CC " i 
5-1 I-H 

I I I I I I I 



o ^ 



43 .a 



e as 

5 ^ 

t- 



a >> 



I 



5-1 51 51 5-1 5-1 51 5-1 51 5-1 51 51 5-1 
51 51 51 51 51 51 51 5-1 51 51 51 5-1 

I 

51 51 CO 1C 51 CO CO 51 CO CO l- O CO 
OOOOOOOOOOO-^O 
+ I + I I I I I ! I I I I 

1- I- 1- O 1- O O I- O O O O t~ 

i-H 1-4 ^H 51 T < 51 51 rH 51 51 51 51 I-H 
r < 51 ^H 51 , I 51 O 51 51 i CO -f IO 

"'+ ! + I I I I I I I I I ! co 

51 

a 
cT 


'51 51 51 51 51 51 51 51 51 51 51 51 5-1 j 

O 

_51 O 51 

* 

OOOOOOOOOOOOr- 

"?! T1 T"! "H C"! I~H rH ^1 i-H f H i-H nH C 1 ! 

1-^* -4-i ^ 

CQ ^ (-, j_ 

j= * * a ^ - ? g o 

O'S'O ^ ^^rSg_gc' 

111! I Ill-si II 



248 COMMANDER L. W. P. CHETWYND: RESULTS OF MAGNETIC OBSERVATIONS, ETC. 
TABLE IV. Declination Results from Swinging Ship at Sea. 



Date. 


Latitude. 


Longitude. 


Greenwich mean 
time of 
observations. 


Declination. 


Observer. 


1907 
10 May 


51 55 N. 


1 48 E. 


h. in. 

5 53 p.m. 


15 33 W. 


W. P.-D. 


16 


54 40 


1 10 W. 


5 16 a.m. 


16 39 




26 


57 


1 50 


5 39 p.m. 


18 45 




9 September. . . . 
19 April 
22 


58 50 
50 29 
50 27 


2 40 

2 32 

2 28 


4 58 
7 42 a.m. 
6 10 p.m. 


19 23 
16 35 

16 40 


M. H. S. 


1 Mav 


51 41 


5 10 


6 42 a.m. 


17 47 




13 


53 1 


5 51 


7 10 


19 7 




13 


53 f> 


5 18 


5 32 p.m. 


18 34 




15 


55 30 


7 35 


24 


20 53 




17 , ... 


56 10 


6 


6 40 a.m. 


20 39 




14 October . . . . 
17 . . . . 


57 57 
57 57 


' 5 23 

5 23 




19 21 
19 9 


JJ 
JJ 



TABLE V. -Comparison of Declination Values Observed at Sea with those from 

Observations made on Shore. 



Date. 


Latitude, 
longitude. 


Declination 
reduced to 
epoch 1st 
January, 


Deduced 
corre- 

Shore station spending 
referred to. value at 
shore 


Value at 
shore 
station 
from obser- 
vations on 


Difference 
from shore 
value. 


Observer. 






1907. 




station. 


shore. 






1907 


' 


- ' 




' 


i 
<. t 


t 




10 May. . . . 51 55 N. 


15 35 AY. Hanvich 15 52 


15 32 +0 20 


W. P.-D. 


1 48 E. 










16 ! 54 50 N. 


16 41 Sunrlerland hi 50 


17 30 -0 40 


- 


I 10W. 










26 .... 57 N. 


18 47 


Stonehaven 19 5 


18 20 +0 45 


)) 


1 50 AY. 












9 September . 58 50 N. 


19 28 Kirkwall 19 28 


19 10 +0 18 


)5 


2 40 AY. 








19 April . . . : 50 29 N. 


16 37 AVeymonth 16 37 


16 51 


-0 14 


M. H. S. 


2 32 AY. 












22 ... 50 27 N. 


16 42 


16 42 


16 51 


-0 9 


Jj 


2 28 W. 












1 May ... 51 41 N. 


17 49 Milford 17 43 


18 9 


-0 26 


)) 




5 10 AY. 










13 ... 


53 21 N. 


19 9 


Dublin 19 21 


19 47 


-0 26 


51 




5 51 W. 












13 ... 


53 26 N. 


18 36 


)? 


19 3 


19 47 


-0 44 


jj 




5 18 AY. 














15 ... 


54 ON. 


18 :', 


Stranraer 1 9 3 


19 35 


-0 32 


j) 




3 36 AY. 














If, ... 


55 30 N. 


20 55 


Letterkenny 


20 50 


20 59 


-0 9 


J> 




7 35 W. 














17 ... 


56 ION. 


20 41 


Loch Melfort 


20 27 


19 51 


+ 36 


jj 




6 W. 














14 October . . 


57 57 N. 


19 26 


Tanera Mor* 


19 31 


20 38 


-1 7 


JJ 




5 23 W. 














17 


57 57 N. 


19 13 


jj 


19 19 


20 38 


-1 19 


J) 




5 23 W. 















See footnote p, 236. 



249 ] 



XI. The Mobilities of the fans produced by Rimtgen Rays in Gases and Vapours. 

By E. M. WELHSCH, M.A. (Sydney], Emmanuel College, Cambridge; Barker 
Graduate Scholar of the University of Sydney. 



Communicated by Prof. Sir J. J. THOMSON, F.R.S. 
Keceived December 19, 1908, Eead January 21, 1909. 

1. Introductory. 

FOR various reasons the determination of the velocities in an electric field of the ions 
produced in gases by the action of Ro'utgen rays is of fundamental importance in 
electrical theory. A knowledge' of the ionic mobilities (i.e. the velocities under unit 
electric intensity) affords information with regard to the structure of the ion ; if, in 
addition, the diffusion coefficients of the ions in various gases are known, the charge 
associated with the ion can be compared with that carried by the monovalent ion in 
the electrolysis of solutions. 

Experimental methods of determining the mobilities of the positive and negative 
ions were devised not long after the ionising action of the Rontgen rays was known. 
RUTHERFORD* determined the values of the sum of the positive and negative 
mobilities in a series of gases. ZELENY,! by comparing the velocity acquired by the 
ions in an electric field with that of a gaseous current parallel to the field, succeeded 
in deducing the values of the difference of the ionic mobilities and also their ratio. 
In later experiments ZEL,ENY| employed a current of gas in a direction perpendicular 
to the electric field and deduced the absolute values of the mobilities in air, oxygen, 
carbon dioxide, and hydrogen. 

No determinations, however, were made of the ionic mobilities in vapours. The 
determination of the physical constants of vapours opened out a considerable field for 

* ' Phil. Mag.,' vol. 44, p. 422 (1897). 
t ' Phil. Mag.,' vol. 46, p. 120 (1898). 
J ' Phil. Trans.,' A, vol. 195, p. 193 (1900). 

For a concise account of the experiments on ionic mobilities vide J. J. THOMSON, " Conduction of 
Electricity through Gases," 2nd edition. 

VOL. CCIX. A 451. 2 K 4.5.09 



250 MR. E. M. WELL1SCH ON THE MOBILITIES OF THE 

theoretical research and afforded rich material for the application of the kinetic theory 
of gases. The measurement of the mobilities of the two kinds of ions formed by the 
action of Rontgen rays in a series of vapours seemed, therefore, to form a fitting and 
necessary continuation of the corresponding determinations in the case of gases ; with 
this object in view the present research was undertaken. 

2. Experimental Method. 

The method employed throughout was that devised by LANGEVIN,* who measured 
the ionic mobilities in air over a range of pressures varying from 7 '5 to 143 cm. of 
mercury. The principle of the method is as follows : 

Suppose we have two parallel plates A and B at a distance d apart, and let there 
be a imiform electric field X in the region between the plates, the force on a positive 
charge being from B to A. Let the gas comprised between them be ionised uniformly 
by a single flash of very short duration from a Rontgen-ray bulb. After the lapse of 
a certain time t from the passage of the Rontgen-ray discharge, let the field between 
A and B be suddenly reversed in direction ; from this time until all the ions have 
been removed by the field A will receive only negative electricity. 

Neglecting effects due to the recombination and diffusion of ions, the total quantity 
of electricity received by the plate A from the time of the Rontgen-ray discharge 
until all the ions are removed is given by 



where Q = quantity of electricity of one sign liberated between the plates by the 

flash of Rontgen rays, 

&j = velocity of the positive ion under unit electric intensity, 
l~ 2 = corresponding velocity for the negative ion. 

By varying the time interval t, a series of values of Q is obtained ; the relation 
between Q and t as given by the above equation is representable by a straight line, 
but this equation has necessarily to be modified by the conditions : 

(i) Each of the quantities kiX.t and & 2 X is to be regarded as zero for negative 
values of t. This implies Q = Q for t < 0. 

(ii) Each of the qiiantities kiKt and & 2 X cannot numerically be greater than d. 
This implies Q = Q for values of t greater than the larger of the two quantities 
and 



With these conditions the relation between Q and t is expressed by a curve of the 
character given in fig. 1. 

* ' Ann. de Chim. et de Phys.,' VII., 28, p. 495 (1903). 



IONS PKODUCED BY RONTGEN RAYS IN GASES AND VAPOURS. 



251 



It is noticeable from the figure that this curve consists of portions of straight lines 
intersecting at points which have as abscissae 0, eZ/& 2 X, d/^X. (for the case k a > X^), 
and which correspond respectively, as far as time considerations are concerned, to the 
momentary Rontgen-ray discharge, the withdrawal of all the negative ions, and the 
receipt of all the positive ions by the plate A. It is evident that, if a curve with the 
above characteristic features .could be obtained experimentally, we could deduce from 
the positions of the points the values of djk^. and dfkyX and thus obtain the 
mobilities of the ions for the gas or vapour under consideration. This procedure 
would not, however, be advisable in practice. The curve in fig. 1 corresponds only to 




I 




TIME 



Fig. 1. 

ideal conditions ; as has been mentioned above, the ionisation must be uniform 
throughout the interval between the two plates, such uniformity being only approxi- 
mately realised in practice ; moreover, LANGEVIN has shown that, as a result of the 
recombination and diffusion of the ions, the effects of which have been neglected in 
the theoretical treatment, the curve as realised experimentally does not consist of 
separate straight lines, but of separate curves which form nicks at their points of 
intersection, the positions of which, however, have not been displaced. 

If the ionisation consist of a uniform distribution between the plates, together with 
a layer of intense secondary ionisation close to the plate A, the theoretical curve 
expressing the relation between Q and t can readily be obtained by adding the 
ordinates due to each part of the ionisation. This curve is shown by the thick lines 
in fig. 2, the thin lines denoting the curve due to the uniform ionisation as before, and 
the dotted lines the curve due to the ionisation localised near the plate A. 

As a result of recombination and diffusion the nicks will be rounded off ; moreover, 
the part QR of the resultant curve is scarcely realisable in practice, especially if there 
be little difference in the values of the two mobilities. In fig. 3 is given the type 

2 K 2 



252 



ME. E. M. WELLISCH ON THE MOBILITIES OF THE 



of curve actually obtained by experiment ; it was obtained under the following 
conditions : 

Gas between electrodes, carbon monoxide at 1 atmosphere. 
X (before reversal) = 387 volts per centimetre. 
Distance between electrodes, 1 cm. 





T/Mt 



/A/ SECl /VOS 



024 



Fig. 3. 

In general, only two points of discontinuous curvature are noticeable, the first 
corresponding to the Rontgen ray discharge and the second to the withdrawal of all 
the ions of one sign, viz., the negative ions if B be at a positive potential before 
reversal and the positive ions if B be at a negative potential before reversal. By 
obtaining experimentally curves for the two cases of B positive before reversal and 
B negative before reversal, we will thus be able to find the negative and positive 
mobilities respectively. 

Taking the case represented in fig. 3, suppose the plate A is connected electrically 
with a similar plate A', whose position with respect to the Rontgen-ray bulb is so 
adjusted that it receives after each discharge a quantity of electricity represented 
graphically by the straight line ABC in the figure. Thus, considering the quantity 
jointly received by the plates A and A', the relation between Q and t will be repre- 
sented by the curve DOE, whose ordinates are obtained by adding those of the two 
curves ABC, LPM ; in other words, as long as t is negative there is, on the whole, no 



IONS PRODUCED BY RONTGEN RAYS IN GASES AND VAPOURS. 253 

charge added to the plates A and A', but as soon as there is any appreciable interval 
between the Rontgen ray discharge and a succeeding reversal of potential on the 
plate B, a charge of electricity is obtained which can be detected by the ordinary 
electrical means, e.g. by connecting the two plates to an electrometer or electroscope. 
In this way the position of the nick at P or of the corresponding point O on the time 
axis can be determined. Tn a similar manner, in order to determine the position of 
the point Q, we would connect the plate A to a plate A', adjusted in such a way as 
to continually receive a charge represented by the straight line FGH in the figure. 
Thus the two plates jointly would receive a charge KST, and the position of S or Q 
could be readily determined by noting the time interval t, on one side of which we 
obtained a charge on the measuring instrument and on the other side of which no 
charge was obtained. 

This null method of obtaining the positions of the nicks in the different curves was 
employed in most of the experiments described in this paper. In actual practice the 
charge given to the auxiliary plate was adjusted in such a way that on one side of 
the nick whose position was sought we obtained a very small constant charge (instead 
of no charge as in the theory), while on the other side^ve would obtain charges of a 
sign opposite to this small charge. By using this method the nicks were well defined 
and thus a high degi-ee of accuracy was obtainable. In addition, it can be readily 
seen that the null method is independent of the intensity of the flash of Rontgen 
rays, whereas, if the complete curve be drawn as in the figure, the flash has to be 
maintained constant in intensity throughout the observations. It is worthy of 
mention that, under the conditions just described, the mobilities are really deter- 
mined for those ions which are formed in the thin layer of gas or vapour in the 
vicinity of the plate A. 

3. Experimental Arrangement. 

The diagram of connections and the disposition of apparatus is given in fig. 4 ; in 
the main it is the same as that used by M. LANGEVIN, but certain necessary modifica- 
tions were introduced to suit the special conditions. 

W and W are two iron weights which are supported by means of an electro- 
magnet ; when the circuit thrcmgh the magnet is broken, the weights fall simultaneously 
and break the platinum contacts at K and K' respectively. The breaking of the 
contact at K', which is in the primary circuit of a Marconi induction coil, gives rise to 
an induced E.M.F. in the secondary, and causes a momentary discharge to pass in the 
Rontgen-ray bulb X ; the breaking of the contact at K reverses the potential of the 
lower plate B of one of the chambers, as can be readily seen from the diagram, R 
being a water resistance of the order of 1 megohm and B at the time of breaking 
being at the same potential as the point /3. K' can be fixed at any point of a vertical 
scale, thus enabling the potential of B to be reversed at any convenient interval 
after the passage of the discharge. This vertical scale was graduated and the 



254 ME. E. M. WELLISCH ON THE MOBILITIES OF THE 

position of K' with regard to K could thus be read off at once ; but when greater 
accuracy was required the position of K ; was ascertained by means of a cathetometer. 
C is a capacity of about 7 microfarads inserted in parallel with the primary of the 
induction coil in order to prevent sparking at the contact K'. When the spark was 
entirely eliminated it was found that, provided the current as measured by the 
ammeter Am was kept constant, the intensity of the Rontgen-ray flash was sensibly 
constant at each discharge. 




VAYWWWWWVW 

AAAAA/W 



Fig. 4. 



AB and A'B' denote the ionisation chambers which are described below ; the upper 
electrodes A and A' could, by means of the key Y, be connected separately to the 
insulated pair of quadrants of an electrometer, or could be connected together either 
with or without connection with the electrometer. The lower plate B' of the chamber 
A'B' is connected with the point b' of the key Z, and from the diagram it can be seen 
that, when I/ and c are joined, B' is permanently earthed, while, when 6' and p are 
joined, B' can be put permanently either at a positive or negative potential by means 
of the key k. The lower plate B of the chamber AB is connected with the point 6 
of the key Z ; thus, when b and e are joined, B is permanently earthed, while, when 
b and m are joined, B is at the potential of the movable arm D of a magnetic 
relay M. When this arm is in contact with the point P, B is thus at zero potential, 
while, when the arm is in contact with Q, B is at the same potential as the point ft, 
a potential which, as above described, is reversed in sign by breaking the contact at 
K. The object of this relay is described below under section 4. 

The potentials necessary to establish the electric fields in the ionisation chambers 



IONS PRODUCED BY RONTGEN RAYS IN GASES AND VAPOURS. 



255 



were obtained from a suitable number of small lead accumulators, the potential 
difference afforded by each being approximately 2 '02 volts. 

The Rontgen-ray bulb was enclosed in a lead-covered box with apertures of 
dimensions sufficient to allow the rays to have access to the chambers. 

For a more detailed account of the essential features of the arrangement the 
reader is referred to LANGEVIN'S original memoir. 




P' 



W/////// / /, ///////////////////////* 



I 



Fig. 5. 

The lonisation Chambers. The two ionisation chambers represented by AB and 
A'B' in fig. 4 were exactly identical in structure and dimensions ; a longitudinal 
section of one of them is shown in fig. 5. The upper electrode A was a brass disc of 
diameter 5 - 91 cm., and was surrounded by a brass guard-ring G, the outer diameter of 
which was 9 cm. A and G were screwed on to an ebonite disc, and A was connected 
to the electrometer by means of a wire led out through an ebonite plug. The 
guard-ring G and the electrode A were separated from the lower electrode B, which 
was of aluminium, by means of an ebonite ring perforated in several places to allow 
the gas or vapour to have free access to the space between the electrodes. The 
distance between A and B was exactly 1 cm. B was connected with the point b of 
the key Z (fig. 4) by means of a wire led out through an ebonite plug, and was kept 
tightly in position by means of the ebonite ring rr. The bottom of the chamber 
consisted of an aluminium disc together with an outer covering of thick lead with 
a central aperture of diameter 3 '56 cm. The Rontgen rays passed through this 
aperture in the lead and through the aluminium constituting both the bottom of the 
vessel and the electrode B ; the gas or vapour between the electrodes was thus ionised, 
and in addition there was strong secondary ionisation produced in the layers of gas 
or vapour in the vicinity of the electrode A. The effect of the outer lead covering 
was to confine the ionisation to the central portion of the interval between the 
electrodes A and B. 



256 MR. E. M. WELLISCH ON THE MOBILITIES OF THE 

P and P' are tubes soldered on to the upper brass covering of the chamber in order 
to afford an entrance for the gas or vapour, and also to admit of the vessel being 
connected to a gauge or pump. In order to keep the vessel air-tight, a rubber band, 
with a mixture of beeswax and resin spread uniformly over its surfaces, was inserted 
between the outer brass and aluminium coverings which, after being heated, were 
screwed tightly together. 

Electrometer. The electrometer was of the Dolezalek pattern with a platinum 
suspension. The needle was charged to a potential of 80 volts, which was found to 
be the voltage most suitable for the conditions of the experiment ; with this potential, 
which did not however correspond to the most sensitive condition, the electrometer 
afforded a deflection per volt of 420 mm. on a scale about 1 metre distant. As a 
matter of fact, an exact determination of the sensitiveness of the electrometer was 
not essential in the present investigation inasmuch as it is only the sign of the 
charge that it is necessary to know in order to determine the points of discontinuous 
curvature referred to in section 2. 

The leads from the upper electrodes to the electrometer quadrants were all screened 
by brass tubing kept at zero potential. 

4. Sources of Error. - A. Theoretical Assumptions. 

Duration of Rdntgen - ray Discharge. It is assumed in the theory that the 
duration of the discharge proceeding from the Rontgen-ray bull) is small compared 
with the time an ion takes to describe the distance between the electrodes. This 
duration has been estimated* to be of the order 10~' second ; the times measured in 
this experiment varied from about O'Ol to 0'03 second. 

Reversal of Potential. After the contact K has been broken, the potential of B is 
reversed in sign ; this reversal necessarily occupies time inasmuch as B has to pass 
through all intermediate potentials. This time is less than the product RC, where li 
denotes the resistance (fig. 4) and C the capacity of the leads and electrode. This 
product in the present case was certainly not greater than 10~ 4 second. 

Influence of the lonisation on the Electrostatic Field. LANGEVIN has shown that 
in the case of uniform ionisation, owing to the distortion of the field by the presence 
of free ions, the time taken by an ion to traverse any distance is increased in a ratio 
numerically inferior to Q /12o-, where Q denotes the total charge of the ions of one 
sign and cr the charge induced on the upper plate when the potential on the lower 
plate is withdrawn. 

For this reason it is advantageous to use, wherever possible, high voltages, but if 
the voltages were made too high, the time taken by the ion to cross the distance 
between the electrodes might become unduly small and the working error propor- 
tionately large. On this account it was difficult to obtain concordant results when 

* BRUNHES, .' Comptes Eendus,' vol. 130, p. 1007, 1900. 



IONS PRODUCED BY RONTGEN RAYS IN GASES AND VAPOURS. 257 

estimating the mobilities at pressures less than 1 cm. of mercury, the workable 
voltages being necessarily small and the field thus being likely to be disturbed by the 
presence of free ions. In general, however, voltages were chosen so as to render the 
influence of the ionisation on the field practically negligible. 

B. Experimental Difficulties. 

Hysteresis. When the magnet circuit is broken, both weights W and W should 
fall simultaneously ; if this occur, the point P in fig. 3 should correspond to a position 
of K' on the movable scale, exactly on a level with the position of K. The position 
of K' corresponding to a zero time interval between the breaking of the two contacts 
could be accurately ascertained by the null method ; in general this position of K' 
occurred when at the same level as K, but after the cells which worked the magnets 
had been in use for a period, usually of about two weeks, it was ascertained that the 
weights did not continue to fall simultaneously, an effect probably due to unequal 
hysteresis in the two magnet cores. In such a case fresh cells were usually inserted, 
but the effect gradually disappeared on reversing the current through the solenoids 
of the magnet. 

Absorption of Charge by the Insulation. If the lower electrode B be at a fairly 
high potential, e.g. 80 volts, and then the potential be reversed, a charge will be 
present on the upper electrode A and its connections ; if now the lower electrode be 
brought back to its original potential, there should on the whole be no free charge 
on A ; with some vapours, however, it was found that a charge remained on A often 
quite considerable in comparison with the charges due to the ionisation of the gas 
when exposed to a flash of Rontgen rays. This residual charge was due to the 
absorption by the insulation of a part of the charge resulting from induction. To 
reduce this absorption to a minimum, use was made of the magnetic relay M (fig. 4). 
As long as the weights W, W remained suspended, the arm D of the relay was in 
contact with the point P, and so the lower electrode B was at zero potential ; but 
when the magnet circuit was broken by the key F, the arm D came in contact with 
the point Q while the weights were still falling freely, and thus the electrode B was 
brought to the required potential. This potential was then reversed by the breaking 
of the contact K, and finally B was brought back to zero potential. By thus restricting 
the period during which B was charged to a very short duration, it was found that 
the effect due to the absorption by the insulation of the charge resulting from induction 
was negligible. 

5. Experimental Procedure. 

The two ionisation chambers were adjusted in such a way that the same flash from 
the Rontgen-ray bulb produced in each equal quantities of electricity of any one sign. 
Preliminary tests were made to ensure that the insulation was good and that there 
was no appreciable absorption of the charge by the insulation. 

VOL. CCIX. A. 2 L 



258 MR. E. M. WELLISCH ON THE MOBILITIES OF THE 

A single reading was then taken in the following manner (the null method being 
employed) : 

(i) K' (fig. 4) is adjusted to the required height on the scale. 

(ii) A and A' are connected together by means of the key Y and are earthed ; the 
quadrants also are at zero potential. In the key Z, b and m are connected, as also 
are b' and p. The contact K is made. 

(iii) The magnet circuit is completed at F ; the weights W and W are placed in 
position ; the movable arm D of the relay M makes contact with P, thus putting B at 
zero potential. 

(iv) A and A' (which throughout remain connected) are insulated ; the quadrants, 
however, remain earthed. 

(v) The contact K' is made ; the magnet circuit is broken at F ; the arm D makes 
contact with Q, thus bringing B to the required potential ; the contact K' is broken 
by W, thus giving rise to a flash of Rontgen rays which ionises the gas in each 
chamber ; after the desired interval the contact K is broken by W, thus reversing the 
potential on the electrode B. 

(vi) By the time the weights have fallen, the ions will have had sufficient time to 
be all received at the electrodes ; the key connecting b and m (in Z) is then removed 
and placed so as to connect b and e, thus bringing B again to zero potential. 

(vii) The quadrant pair is insulated ; the deflection due to the total charge received 
by A and A' is then observed and noted. 

When the potential V is established on the electrode B, the upper electrode system 
AA' will be raised to a potential r proportional to V. The value of v corresponding 
to any definite potential V was determined experimentally in the following manner. 
The upper electrode system was connected to the electrometer and the steady deflection 
d was noted when B was raised to the potential V. The quadrants were then earthed 
and the upper electrode system was charged to a known small potential v' by means 
of a potentiometer ; the system was then disconnected from the potentiometer and 
connected to the insulated uncharged quadrant pair, causing a steady deflection d'. 
The potential v' was then varied until d' became equal to d ; this value of v' 
corresponds to the required potential v. As a result of a series of observations with 
different values of V, it was deduced that when the electrode B was raised from zero 
potential to a potential of V volts, the upper electrode system attained a potential of 
0-0425 V volt.* 

The corresponding electric field, which was sensibly uniform in the region to which 
the ionisation was confined, was thus 0'9575 V volt per centimetre. 



* The potential v should also be given by fl/diS, where d denotes the steady deflection as above, d\ 
denotes the steady deflection resulting from reconnecting the upper electrode system to the quadrants after 
they have been earthed and insulated, and 8 denotes the sensitiveness of the electrometer over the range 
of deflections under consideration. A series of observations led to the same result as above. 



IONS PRODUCED BY RONTGEN RAYS IN GASES AND VAPOURS. 



259 



The actual potentials of B and B' during the experiment will, of course, depend, as 
above explained (section 2), on the particular nick in the curve whose position is sought ; 
these potentials are controlled by means of the key k, and also by adjustable connections 
(s and s') at the battery. 



+15 





!-= 
I 

s 

5-10 

I 



15 



10 



S! 



-5 



006 -012 -018 

TIME w SECONDS 



-024 



050 



3 O O 



006 -0^ -018 -04 

TIME. IN SECONDS. 



030 



Fig. 6. Fig. 7. 

In fig. 6 and fig. 7 are given typical curves which were obtained by the null method 
from observations made to determine the position of the nicks corresponding to the 
negative and positive velocities respectively in sulphur dioxide at a pressure of 
269 mm. of mercury, the electric field being 387 volts per centimetre. 

6. Manipulation of Gases and Vapours. 

The atmospheric air employed was dried by passing through phosphorus pentoxide. 

The nitrous oxide and carbon dioxide were obtained from cylinders of compressed 
gas and were dried by passing through phosphorus pentoxide. 

The ammonia was obtained from a cylinder of the compressed gas and was dried by 
passing through solid potassium hydroxide. 

The carbon monoxide was liberated by the action of sulphuric acid on sodium 
formate and was dried by passing through phosphorus pentoxide. 

The sulphur dioxide was liberated by the action of dilute sulphuric acid on sodium 
sulphite and was dried by passing through calcium chloride. 

The vapours employed were, in most cases, dried according to the method followed 
by W. H. PERKIN* in his investigation of the " Magnetic Rotary Polarisation 01 
Compounds in relation to their Chemical Constitution." In all cases Kahlbaum's 
preparations were used. 

The ethyl alcohol, methyl acetate, ethyl formate, and ethyl acetate were from samples 
kindly lent me by Mr. T. H. LABY, who had previously obtained them by fractionating 
and drying Kahlbaum's preparations till each sample had a constant boiling-point. 



* ' Journ. Chem. Soc. Trans.,' vol. 45, p. 421, 1884. 
2 L 2 



260 MR. E. M. WELLISCH ON THE MOBILITIES OF THE 

In addition to the ethyl ether obtained from Kahlbaum ether from another source 
was fractionally distilled three times, the last time with metallic sodium, and the 
portion boiling at 35'2 C. (barometer 769 mm.) was collected and used. The resulting 
mobilities were in concordance with those previously obtained. 

The ionisation chambers were exhausted by means of a Topler mercury pump ; in the 
case of a gas it was admitted to the pump and the pressure could be diminished or 
increased with comparative ease ; in the case of a vapour the pump was first of all 
disconnected by means of a tap and the liquid allowed to evaporate into the apparatus 
till the requisite pressure was obtained. Often a stream of vapour was passed 
through by means of a water pump, thus ensuring that any air which had remained 
in the apparatus was removed. 

As is usually the case when working with vapours, the pressure at first decreases 
owing to partial condensation ; it, however, ultimately reaches a steady state. It is 
possible, moreover, that some chemical action between the vapour and the metal of 
the ionisafcion chambers might interfere with the mobility values ; the best way of 
investigating this point is to find the ionic mobilities in the vapour under conditions 
as varied as possible. In certain instances the values obtained were not concordant ; 
these values are given in the table of results, Imt are not used in calculating the 
mean mobilities. In general, however, the values obtained over widely different 
conditions were in good agreement. 

The pressures were measured by means of a mercury gauge, one limb of which had 
been previously exhausted to a high vacuum by means of the Topler pump and then 
sealed ; in this manner the pressure readings were made independent of the barometric 
reading. 

7. Experimental Results. 

In estimating the ionic mobilities in a gas or vapour, it is important to secure as 
wide a variation as possible in the experimental conditions ; such a variation was 
obtained in the following ways : 

(i) The mobilities were estimated in different samples of the gas or vapour. 

(ii) The mobilities were often measured in each of the two ionisation chambers, the 
remaining one in each case serving as the standard. 

(iii) The electric field was made to vary over as wide a range as was practicable. 

(iv) The mobilities were measured over a wide range of pressures. 

(v) The experiments were often repeated after a lapse of several weeks, other gases 
or vapours having in the meantime been experimented upon. 

Under conditions so varied it was only to be expected that variations should occur 
in the mobility values ; most of the variations were within 7 per cent, of the mean 
value. The actual experimental conditions and the results obtained are exhibited in 
the following tables ; the values apply to a mean temperature of about 15 C., but it 



IONS PEODUCED BY RONTGEN RAYS IN GASES AND VAPOURS. 261 

will be noticed that, although the actual temperatures are given, no correction has 
been made, as such correction would almost certainly lie within the limits of error of 
the experiment. 

The figures in the second column give the electric field X in volts per centimetre. 
The third and fourth columns give the height in centimetres from the bottom of the 
falling weight W to the movable contact K', when the latter is in the positions 
corresponding respectively to the first and second nicks in the typical curve (vide 
fig. 3, which was obtained in the measurement of a negative mobility). The fifth 
column contains the equivalent time interval / expressed as the fraction of a second ; 
it was calculated by means of the ordinary formula for a body falling freely under 
gravity. The values in centimetres per second of the mobility k are calculated from 
the equation k = 1/X^, and, corresponding to the stated pressure, are given in the 
seventh column. In the eighth and ninth columns are given the mobilities corre- 
sponding to a potential gradient of 1 volt per centimetre and to a pressure of 760 mm. 
of mercury ; these values are based on the assumption that the ionic velocity is 
proportional to the field intensity and is inversely proportional to the pressure. 

An asterisk affixed to a mobility value denotes that this value was not included in 
estimating the mean ; these values showed marked deviations from the law 
pk = constant, the reasons for these deviations in some cases not being apparent, but 
in most cases being due to the pressures lying outside the range for which the law is 
applicable. 



rr, TTI i Height of fall to 

Tern- Electric ___ T . p ; 

perature. field. lgt ^.^ 2nd point + 

C. volts/cm. cm. cm. sec. mm. om./sec. cm. /sec. cm. /sec. 

Am. 
14 38-7 54-8 50-0 0-0150 758 1'72 1'7 



50-0 


0-0150 


758 


1-72 




49-5 


0-0166 


758 


1-56 


1-55 


50-0 


0-0150 


762 


1-72 




49-5 


0-0166 


762 


1-56 


1-56 


52-5 


0-0071 


380 


3-64 




52-1 


0-0083 


380 


3-11 


1-56 


50-3 


0-0140 


760 


1-85 




49-5 


0-0166 


760 


1-56 


1-56 


50-7 


0-0127 


264 


5-08 




50-0 


0-0150 


264 


4-30 


1-49 


51-0 


0-0118 


98 


14-61 




50-0 


0-0150 


102 


11-59 


1-54* 



16-5 

49-5 0-0166 762 1-56 1-56 

1-82 

1-85 

15-5 50-7 0-0127 264 5'08 1-76 

50-0 0-0150 264 4-30 1'49 

5-8 51-0 0-0118 98 14-61 1'88* 



, , , , [' positive ion 1 54 cm./sec. 

Mean values of *-, { egative >f j.yg / ( 



262 ME. E. M. WELLISCH ON THE MOBILITIES OF THE 

T,, , . Height of fall to &7eo- 

Tern- Electric * _. Time p res sure. *. , . 

perature. field. lst point . 2 nd point. + 

C. voifcs/cm. cm. cm. sec. mm. cin./sec. cm./sec. om./ec. 

CARBON MONOXIDE. 

14 38-7 54-8 51'3 0-0108 355 2-39 1-12 

19-3 48-5 0-0198 347 2-62 1-19 

51-2 0-0112 173 4-63 1'05 

13 38-7 47-8 0-0221 759 1-17 1'17 

51-2 0-0112 361 2-31 1'09 

51-5 0-0102 361 2-53 1-20 

19-3 50-7 0-0127 201 4'08 1-08 

50-9 0-0121 201 4-28 1-13 

7-7 50-4 0-0137 93 9-48 1-16 

50-4 0-0137 93 9-48 M6 

3-9 51-5 0-0102 34 25-13 1'12 

51-0 0-0118 36 21-72 1'03 



T,, e , f positive ion 1-10 cm./sec. 

Meanvaluesof ^( negative M4 



CARBON DIOXIDE. 

15 77-4 55-0 50-2 0-0149 754 0-87 0-86 

50-0 0-0156 754 0'83 0-82 

38-7 54-8 52-2 0-0080 200 3-23 0'85 

52-1 0-0083 200 3-11 0'82 

77-4 49-8 0-0156 760 0'83 0-83 

49-5 0-0166 760 0'78 0'78 

17-4 53-2 0-0049 60 11-73 0'93* 

53-0 0-0055 60 10-45 0'82* 



,., c , f positive ion 0-81 cm./sec. 

Mean values of fenn"! * n o- 

u \negative 0'8o 



NITROUS OXIDE. 

15 77-4 55-0 50-4 0-0143 754 0'90 0'90 

0'86 

0'89 

0'83 

0-91 

16 19-3 49-3 0-0178 241 2-91 0'92 

0'81 

5-8 51-0 0-0124 51 13-91 0-93* 

0-86* 

17 38-7 54-8 45'5 0-0297 791 0-87 0'91 

0'90 

19-3 50-8 0-0124 167 4-18 0'92 

38-7 46-0 0-0280 741 0-92 0-90 

0-80 
15-5 45-5 0-0297 307 2-17 0-88 

0-81 

1-9 50-0 0-0150 23 35-08 1'06* 

0'96* 



i 50-4 


0-0143 


754 


0-90 


50-2 


0-0149 


754 


0-87 


50-3 


0-0146 


766 


0-88 


50-0 


0-0156 


766 


0-83 


50-4 


0-0143 


762 


0-90 


49-3 


0-0178 


241 


2-91 


48-5 


0-0204 


241 


2-54 


51-0 


0-0124 


51 


13-91 


50-7 


0-0134 


51 


12-87 


i 45-5 


0-0297 


791 


0-87 


49-7 


0-0159 


419 


1-62 


50-8 


0-0124 


167 


4-18 


46-0 


0-0280 


741 


0-92 


45-0 


0-0314 


741 


0-82 


45-5 


0-0297 


307 


2-17 


44-8 


0-0320 


307 


2-02 


50-0 


0-0150 


23 


35-08 


49-5 


0-0166 


23 


31-70 


Mean values of k-, 


f positive 


ion 0-82 


cm./sec. 




l_ negative 


s 0-90 


>! 



IONS PRODUCED BY RONTGEN RAYS IN GASES AND VAPOURS. 263 

Tern- Electric Height of fall to * 760 . 

perature. field. Tlme " Insure. k. 

1st point. 2nd point. .(- 

C. volts/em. om. cm. seo. mm. cm./sec. cm /sec. cm./sec. 



AMMONIA. 



13 
14 


77-4 
38-7 

77-4 
38-7 

19-3 

38-7 


54-9 

54-8 



13 



15 
13 



38-7 



19-3 



38-7 



19-3 



50-8 


0-0127 


602 


1-02 




0-81 


50-5 


0-0136 


590 


0-95 


0-74 




49-6 


0-0162 


348 


1-59 


0-73 




50-0 


0-0150 


348 


1-72 




0-79 


52-4 


0-0074 


350 


1-75 




0-80 


50-7 


0-0127 


294 


2-03 




0-79 


50-3 


0-0140 


296 


1-85 


0-72 




50-3 


0-0140 


162 


3-70 




0-79 


50-0 


0-0150 


162 


3-45 


0-74 




49-3 


0-0172 


408 


1-50 




0-81 


49-2 


0-0175 


387 


1-48 


0-75 





Mean values of k m ( P sit j ve ion ' J* cm '/ sec - 
]_ negative 0-80 



ALDEHYDE. 



54-8 



49-7 


0-0159 


145 


1-62 


50-1 


0-0146 


137 


1-77 


50-7 


0-0127 


109 


2-03 


50-6 


0-0131 


107 


1-97 


47-2 


0-0240 


107 


2-16 


47-7 


0-0224 


103 


2-31 


50-4 


0-0137 


57 


3-78 


50-8 


0-0124 


57 


4-18 


46-7 


0-0257 


223 


1-01 


46-7 


0-0257 


219 


1-01 


46-6 


0-0260 


240 


99 


47-0 


0-0247 


238 


1-05 


49-3 


0-0172 


164 


1-50 


49-0 


0-0182 


164 


1-42 


49-3 


0-0172 


78 


3-01 


49-1 


0-0179 


78 


2-89 



AT c , f positive ion 0'31 cm. /sec. 

Mean values of* | Negative 0-30 ,, 



0-32 
0-29 



0-31 

0-31 

0-29 



0-33 
0-32 

0-31 



0-31 



0-28 
0-30 

0-28 



0-30 
0-31 



0-31 
0-30 



ETHYL ALCOHOL. 



16 



9-7 

7-7 

9-7 



54-8 



51-2 


0-0112 


24 


9-20 


51-7 


0-0096 


24 


10-74 


50-6 


0-0131 


26 


9-91 


49-3 


0-0172 


26 


7-55 


50-6 


0-0131 


26 


9-91 


49-3 


0-0172 


26 


7-55 


50-8 


0-0124 


26 


8-31 


51-5 


0-0102 


26 


10-11 



, c , f positive ion 0-34 cm./sec. 
Mean values of *r ( egative -27 ,, 



0-34 
0-34 

0-34 



0-35 



0-29 



0-26 

0-26 
0-28 



264 

Tern- Electric 
perature. field. 

C. Yolts/cm. 



MR. E. M. WELLISCH ON THE MOBILITIES OF THE 
Height of fall to 



1st point. 2nd point. 



Time. 



Pressure. 



k. 



&760- 



cm. /sec. cm. /see. cm. /sec. 



ACETON. 



20 



15-5 



38-7 
19-3 



13-5 
38-7 

19 3 



15-5 

9-7 

19-3 



55-0 



54-8 



48-7 


0-0198 


69 


3-26 


49-3 


0-0178 


69 


3-62 


49-2 


0-0181 


65 


3-56 


52-6 


0-0074 


65 


3-49 


51-0 


0-0118 


56 


4-39 


50-3 


0-0140 


58 


3-70 


49-0 


0-0182 


84 


2 85 


49-3 


0-0172 


52 


4 32 


50-8 


0-0124 


106 


2-08 


51-3 


0-0108 


106 


2-39 


49-4 


0-0109 


78 


3-07 


48-7 


0-0191 


82 


2-71 


48-5 


0-0198 


82 


2-62 


50-0 


0-0150 


54 


4-30 


1 9 5 


0-0160 


35 


0-21 


50 


0-0150 


35 


6-87 


50-2 


0-0143 


73 


3-62 


50-6 


0-0131 


73 


3-95 



,. c , f positive ion 0-31 cm. /sec. 

Mean values of brm< t 

\ negative 



0-33 
0-31 
0-29 



0-32 
0-38* 



0-30 



0-33 


s. 


0-30 






0-30 


0-32 






0-28 


0-31 






0-29 




0-29 



0-28 
0-31 
0-29 

0-35* 



0-29 



SULPHUR DIOXIDE. 



19 



77-4 

38-7 
19-3 

116-0 
77-4 
38-7 

154-7 
15-5 



54-8 



55-0 



48-4 


0-0201 


487 


0-64 


49-0 


0-0182 


483 


0-71 


48-7 


0-0191 


459 


0-68 


49-0 


0-0182 


457 


0-71 


48-2 


0-0208 


269 


1-24 


47-5 


0-0230 


269 


1-12 


46-0 


0-0280 


170 


1-85 


46-6 


0'0260 


170 


1-99 


50-6 


0-0131 


496 


0-66 


50-8 


0-0124 


489 


0-69 


49-0 


0-0182 


464 


0-71 


48-7 


0-0191 


454 


0-68 


48-0 


0-0214 


247 


1-20 


48-5 


0-0198 


247 


1-30 


49-9 


0-0153 


711 


0-42 


50-3 


0-0140 


711 


0-46 


49-9 


0-0158 


79 


4-08 


50-4 


0-0143 


79 


4-51 



Mean values of * 



("positive ion 0-44 
'L negative 0-41 



0-45 

0-43 
0-44 



0-45 

0-45 
0-43 



0-42 
0-43 
0-47 



0-41 
0-41 



0-40 
0-41 

0-43 



0-40 
0-39 

0-39 
0-42 



IONS PRODUCED BY RONTGEN RAYS IN GASES AND VAPOURS. 

Height of fall to k m . 



265 



Tern- Electric 
perature. field. lst point . 2n d point. 

C. volts/em. cm. cm. 



Time. 



Pressure. 



cm./iec. cm. sec. 



14 
13 
15 

13 
14 



77-4 



38-7 
77-4 



54-8 



P>THYL CHLORIDE. 



Table I. 



46-7 


0-0257 


419 


0-50 


46-9 


0-0250 


407 


0-52 


47-0 


0-0247 


374 


0-52 


47-3 


0-0237 


364 


0-54 


48-2 


0-0208 


338 


0-62 


48-3 


0-0204 


333 


0-63 


48-9 


0-0185 


324 


0-70 


48-7 


0-0191 


316 


0-68 


49-8 


0-0156 


256 


0-83 


50-6 


0-0131 


221 


0-99 


50-7 


0-0127 


220 


1-02 


47-4 


0-0234 


205 


1-10 


51-1 


0-0115 


203 


1-12 



,, , , , f positive ion O'L'9 cm. /.sec. 

Mean values of ft { egative . 28 ,< 



0-28 
0-26 

0-30 

0-28 

0-29 
0-30 
0-30 



0-28 
0-26 

0-28 
0-28 

0-28 
0-29 



Table II. 



15 
13 



77-4 



38-7 



5-8 

7-7 
3-9 

5-8 



54-8 



50-5 


0-0134 


232 


0-96 




50-9 


0-0121 


230 


1-07 


0-32 


51-4 


0-0105 


201 


1-23 




51-6 


0-0099 


199 


1-31 


0-34 


51-5 


0-0102 


196 


1-27 


0-33 


51-5 


0-0102 


193 


1-37 




48-1 


0-0211 


186 


1-22 




51-4 


0-0105 


103 


2-46 


0-33 


51-8 


0-0093 


91 


2-78 


0-33 


51-9 


0-0090 


83 


2-87 




46-6 


0-0260 


36 


6-63 




50-0 


0-0150 


22 


11-50 


0-33 


50-9 


0-0121 


22 


10-73 




49-9 


0-0153 


16 


16-76 


0-35 


49-5 


0-0166 


16 


15-44 




51-2 


0-0112 


16 


15-40 




51-7 


0-0096 


15 


17-96 


0-35 



, , f positive ion 0-33 cm. /sec. 
Mean values of k 7W | egative n . ql 



0- 



The explanation of this double tabulation of values is given later under section 8. 
VOL. CCIX. A. 2 M 



0-29 
0-33 



0-32 
0-30 



0-31 
0-31 

0-31 

0-32 
0-32 



266 



MR. E. M. WELLISCH ON THE MOBILITIES OF THE 



, T7i i Height of fall to 

leni- Electric 



perature. I7t point. 2nd point. 



C. volts/cm. cm. 



Time. 



Pressure. 



k. 



mm. cm./sec. cm. /sec. 



cm. I tee. 



PENTANE. 



14 



13 



14 



19-5 



20-5 



38-7 

19-3 
38-7 

77-4 
38-7 
77-4 



19-3 
38-7 
19-3 
15-5 



54-8 



48-0 


0-0214 


217 


1-21 


0-34 




48-2 


0-0208 


215 


1-24 


0-35 




49-4 


0-0169 


171 


1-53 




0-34 


49-3 


0-0172 


173 


1-50 


0-34 




49-3 


0-0172 


173 


1-50 




0-34 


50-8 


0-0124 


67 


4-18 


0-37 




50-8 


0-0124 


67 


4-18 




0-37 


47-5 


0-0230 


228 


1-12 




0-34 


48-0 


0-0214 


222 


1-21 


0-35 




48-2 


0208 


222 


1-24 




0-36 


48-4 


0-0201 


218 


1-28 


0-37 




48-2 


0-0208 


216 


1-24 




0-35 


49-5 


0-0166 


370 


0-78 


0-38 




49-5 


0-0166 


366 


0-78 




0-37 


50-8 


0-0124 


128 


2-08 




0-35 


50-8 


0-0124 


128 


2-08 


0-35 




50-3 


0-0140 


302 


0-92 




0-37 


50-3 


0-0140 


302 


0-92 


0-37 





,. , f , I positive ion 36 cm. /sec. 

Mean values of fc( egative ^ Q . 35 / 



METHYL ACETATE. 



54-8 



55-0 



49-8 


0-0156 


86 


3-32 


49-7 


0-0159 


84 


3-26 


51-3 


0-0108 


100 


2-39 


51-6 


0-0099 


99 


2-61 


49-6 


0-0162 


80 


3-20 


49-4 


0-0169 


78 


3-07 


49-5 


0-0172 


70 


3-75 


49-8 


0-0162 


71 


3-98 



Ar , c , f positive ion 0-33 cm./sec. 

Mean values of faml * .. n oc 

L negative 36 



0-36 
0-31 



0-31 
0-34 



0-38 



0-34 
0-34 



0-37 



ETHYL FORMATE. 



20-5 



19-3 

38-7 
19-3 



38-7 
19-3 



54-8 


48-9 


0-0185 


87 


2-80 




48-9 


0-0185 


87 


2-80 




50-9 


0-0121 


114 


2-13 


55-0 


48-4 


0-0207 


93 


2-50 




48-8 


0-0194 


83 


2-87 




49-3 


0-0178 


83 


2-91 


54-8 


48-0 


0-0214 


93 


2-42 




51-4 


0-0105 


91 


2-46 




51-4 


0-0105 


91 


2-46 




48-5 


0-0198 


89 


2-62 




48-5 


0-0198 


89 


2-62 



M i {7 f positive ion 0- 30 cm. /sec. 

Mean values of A i * ,. 

u \negative 0-31 



0-32 



0-29 



0-29 
0-31 



0-32 
0-32 
0-31 

0-32 
0-30 
0-29 



0-31 



Tem- 
perature. 



IONS PRODUCED BY RONTGEN RAYS IN GASES AND VAPOURS. 
Electric Hei S ht of fal1 to 



267 



field. 



1 C. Yolts/cm. 



1st point. 2nd point. 



Time. 



Pressure. 



k. 



cm./sec. cm./sec. 



em. /sec. 



ETHYL ETHER. 



10 

19 

18-5 

9 



19 



38-7 



13-5 

7-7 
38-7 



9-7 

5-8 



19-3 



54-8 


49-5 


0-0166 


154 


1-56 




0-32 




49-2 


0-0175 


154 


1-48 


0-30 






50-6 


o-otsi 


110 


1-97 


0-29 






50-7 


0-0127 


114 


2-03 




0-30 




48-5 


0-0198 


176 


1-30 




0-30 




51-3 


0-0108 


94 


2-39 




0-30 


54-9 


48-0 


0-0217 


200 


1-19 




0-31 




47-6 


0-0230 


198 


1-12 


0-29 






46-5 


0-0267 


234 


0-97 




0-30 


54-8 


48-9 


0-0185 


159 


1-40 




0-29 




48-9 


0-0185 


155 


1-40 


0-28 






49-5 


0-01GG 


58 


4-46 




0-34 




49-0 


0-0182 


32 


7-13 




0-30 




50-3 


0-0140 


137 


1-85 




0-33 




49-2 


0-0175 


176 


1-48 




0-34 




49-2 


0-0175 


157 


1-48 


0-30 






46-6 


0-0260 


204 


0-99 




0-27 




46 -6 


0-0260 


198 


0-99 


26* 





,, r , f positive ion 0'29 cm./sec. 

Mean values of 7 ,, | | iegatiye ^ Q . 31 ;/ 



ETHYL ACETATE. 



54-8 



50-3 


0-0140 


28 


7-36 




50-9 


0-0121 


28 


8-52 


0-31 


48-2 


0-0208 


28 


8-29 


0-30 


47-9 


0-0217 


28 


7-94 




51-2 


0-0112 


46 


4-63 




51-5 


0-0102 


46 


5-08 


0-31 



,. - , f positive ion 0'31 cm./sec. 

Mean values ot k-,- M < f 

\ negative 0-28 ,, 



0-27 



0-29 
0-28 



METHYL BROMIDE. 



22 



77-4 

38-7 
19-3 
13-5 



55-0 



46-5 


0-0270 


404 


0-48 




47-5 


0-0237 


384 


0-54 


0-27 


49-3 


0-0178 


296 


0-73 


0-28 


49-2 


0-0181 


298 


0-71 




50-5 


0-0139 


125 


1-86 




50-6 


0-0136 


125 


1-90 


0-31 


51-0 


0-0124 


57 


4-18 


0-31 


50-7 


0-0134 


59 


3-86 




50-3 


0-0146 


42 


5-07 




50-7 


0-0134 


42 


5-53 


0-30 



,, t ; f positive ion 29 cm./sec. 

Mean values of *roo { egative f> -28 

2 M 2 



0-25 



0-28 
0-31 



0-30 
0-28 



268 ME. E. M. WELLISCH ON THE MOBILITIES OF THE 

, , . Height of fall to b; W . 

Tern- Electric _ . , Time . Pressure. *. 

perature. field. 

C. Tolts/cm. cm. cm. sec. mm. cm./sec. cm./sec. cm./sec. 



10 38-7 54-9 47-0 0-0250 178 1-03 0-24 

77-4 50-2 0-0146 182 0-88 0-21 

38-7 51-2 0-0114 74 2-27 0-22 

0-20 

0-20 

19-3 54-8 53-0 0-0055 18 9-42 0-22 

0-21 

0-22 
0-21 



1st point. 2nd point, 
cm. cm. 


sec. 


mm. 


cm./sec. 


METHYL IODIDE. 


54-9 


47-0 


0-0250 


178 


1-03 




50-2 


0-0146 


182 


0-88 




51-2 


0-0114 


74 


2-27 




50-9 


0-0124 


74 


2-08 




47-3 


0-0240 


138 


1-08 


54-8 


53-0 


0-0055 


18 


9-42 




53-3 


0-0046 


14 


11-26 




51-6 


0-0099 


64 


2-61 




51-4 


0-0105 


64 


2-46 


Mean v< 


lines of k-, 


I" positive ion 
'" \ negative 


21 cm./sec. 
22 


CARBON TETRACHLORIDE. 


54 8 


50-5 


0-0134 


43 


5-53 




50-5 


0-0134 


43 


5-53 




49-8 


0-0156 


39 


4-75 




50-0 


0-0150 


39 


4-94 


55-0 


50-6 


0-0136 


34 


7-58 




50-3 


0-0146 


56 


4-42 




50-3 


0-0146 


59 


4-42 




50-3 


0-0146 


59 


4-42 




50-6 


0-0136 


32 


7-58 




50-9 


0-0128 


48 


5-04 




50 7 


0-0134 


48 


4-82 


Mean 


values of 


f positive ion 
160 \negative ,, 


30 cm. 
0-31 


/sec. 






ETHYL IODIDE. 






54 9 


52-4 


0-0077 


31 


3-36 




52-7 


0-0068 


31 


3-80 


54-7 


49-8 


0-0153 


37 


3-39 




49-3 


0-0169 


37 


3-06 


54 -S 


49-8 


0-0156 


41 


3-32 




49-6 


0-0162 


41 


3-18 




48-3 


0-0204 


53 


2-54 




48-1 


0-0211 


53 


2-45 


54-9 


49-8 


0-0159 


31 


3-26 




48-8 


0-0191 


29 


2-71 



11 13-5 54-8 50-5 0-0134 43 5-53 0-31 

0-31 
0-24 

0-25 
0-34 

15-5 50-3 0-0146 56 4-42 0'33 

0-34 

0-34 
20 9-7 50-6 0-0136 32 7-58 0-32 

15-5 50-9 0-0128 48 5-04 0'32 

0-30 



10 38-7 54-9 52-4 0-0077 31 3-36 0-14 

0-15 
19-3 54-7 49-8 0-0153 37 3-39 0-16 

0-15 
16 54-S 49-8 0-0156 41 3-32 0-18 

0-17 
0-18 

0-]7 
10 54-9 49-8 0-0159 31 3-26 0-13* 

0-10* 

AT r, f positive ion 0-17 cm. /sec. 

Mean values of K-rmi ,.- n ic 

l_ negative O'lo 

In the following table is given a summary of the results obtained for the ionic 
mobilities ; they correspond to an electric intensity of 1 volt per cm. and a pressure 
of 760 mm. of mercury. There is appended a table containing the values of the 
mobilities previously ascertained. 



IONS PRODUCED BY RONTGEN RAYS IN GASES AND VAPOURS. 



269 



TABLE I. Summary of Ionic Mobilities. 



Gas or vapour. 


Formula. 


Molecular 
weight. 


Absolute 
critical 
temperature. 


h 
+ 


no- 


Air 
Carbon monoxide .... 
Carbon dioxide 


CO 
C0 2 


28 
44 


"C. 

137 
304 


em. /sec. 

1-54 
1-10 
0-81 


cm. /sec. 
1-78 
1-14 
0-85 


Nitrous oxide 


N.>O 


44 


310 


0-82 


0-90 


Ammonia 
Aldehyde 
Ethyl alcohol 


NH 3 
C 2 H 4 
CoH c O 


17 
44 
46 


404 
454 
513 


0-74 
0-31 
0-34 


0-80 
0-30 
0-27 


Aceton 
Sulphur dioxide .... 
Ethyl chloride 
Pentane 
Methyl acetate 


C 3 H 
S0 2 
C,H 5 C1 
C 6 H 12 
CsH/), 


58 
64 
64-5 

72 
74 


511 
429 
458 
470 

507 


0-31 
0-44 
0-33 
0-36 
0-33 


0-29 
0-41 
0-31 
0-35 
0-36 


Ethyl formate 


C 3 H ti O, 


74 


507 


0-30 


0-31 


Ethyl ether 


C 4 H 10 O 


74 


467 


0-29 


0-31 


Ethyl acetate .... 


C 4 H 8 0, 


88 


522 


0-31 


0-28 


Methyl bromido .... 
Methyl iodide 


CH,Br 
CH 3 I 


95 
142 


467 
528 


0-29 
0-21 


0-28 
0-22 


Carbon tetrachloride . 
Ethyl iodide 


CC1 4 

C.,H S I 


154 
156 


557 
554 


0-30 
0-17 


0-31 
0-16 















TABLE II. Mobilities Previously Ascertained. 



f1__ 




Molecular 


Absolute 


h 


60- 




vras. 




weight. 


temperature. 


+ 


- 




Air 

M 


Hydrogen 


H 


2 


C. 
35 


cvu./sec. 
1-36 
1-60 
1-39 
6-70 


cm. /sec. 

1-87 
1-70 
1-78 
7-95 


ZELENY. 
LANGEVIN. 
PHILLIPS. 
ZELENY. 


Helium 


He 


4 


4-5 


5-09 


6-31 


FRANCK and POHL. 


Nitrogen 
Oxygen 
Hydrochloric acid . . 
Carbon dioxide . . . 
M ... 
Sulphur ,, ... 
Chlorine 


N 8 
2 
HC1 
C0 2 



SO, 
Clo 


28 
32 
36-5 
44 

64 

71 


124 
154 
325 
304 

429 
414 


1- 
1-36 
I- 

0-76 
0-86 

o- 

1- 


6* 
1-80 
27* 
0-81 
0-90 
5* 
[)* 


RUTHERFORD. 
ZELENY. 
RUTHERFORD. 
ZELENY. 
LANGEVIN. 
RUTHERFORD. 
RUTHERFORD. 

















* Mean values. 



270 MR. E. M. WELLISCH ON THE MOBILITIES OF THE 

8. Discussion of Results. 

A first deduction from the experimental results is that for a given electric intensity 
the velocity of an ion varies inversely as the pressure ; while, for a constant pressure, 
the velocity is directly proportional to the electric intensity. 

LANGEVIN found that in air over a range of pressures varying from 7 '5 cm. to 
143 cm. of mercury the product of the pi-essure and the mobility of the positive ion 
was sensibly constant ; but, in the case of the negative ion, this product showed a 
marked increase in value when the pressure was reduced below 20 cm. ; this result 
was interpreted as denoting a simplification in the structure of the negative ion at 
relatively low pressures. The values of the mobilities given for CO 2 and N 2 O in the 
tables show an increase in the product pk at low pressures both for the positive and 
negative ions. As pointed out before, the experimental ei'ror tends to increase when 
the mobilities are measured at low pressures ; on this account no attempt was made 
to obtain measurements at pressures below 1 cm. of mercury. 

In the case of vapours the pressures were in general chosen so that the vapour 
under consideration was well removed from its condensation point ; under these 
circumstances no tendency of the product pk to increase with diminution of pressure 
was observed. However, attempts were made to observe whether there was any 
deviation from the law pk = constant as the vapour approached the saturated state ; 
great difficulty was incurred on account of the tendency of the vapour to condense 
on the insulation, nevertheless, in the case of ethyl chloride, the product pk 
showed a marked decrease in value both for the positive and negative ions as the 
pressures were increased beyond 200 mm.* It is known from experiments on 
saturated vapours f that the density of a vapour increases more rapidly than 
would be expected from BOYLE'S law as the vapour approaches saturation, in other 
words, there is a tendency for the vapour molecules to form aggregations ; this 
would result in a diminution of the value of the product pk, either in consequence 
of an increased complexity of the ionic structure, or of an increased collision 
frequency between the ion and the molecules of the vapour. Another explanation 
of the alteration in value of pk is given below, under section 9 ; on this view the 
alteration depends not so much on the increase of density as on the marked increase 
in viscosity which has been shown! to occur when a vapour approaches the saturated 
state. 

PRZIBRAM has recently measured the ionic mobilities in several vapours at a 
pressure of 1 atmosphere, the temperatures being chosen so as to just suffice to 
prevent condensation ; the vapours were ionised by the a rays from polonium, and a 

* The vapour pressure of ethyl chloride at 10 C. is 691 mm. 

t Cf. MEYER, ' Kinetic Theory of Gases,' 2nd edition, chapter 4. 

{ Cf. MEYER, loc. til., chapter 7. 

' Wien. Berichte,' Ila, Bd. 117, p. 665, 1908. 



IONS PRODUCED BY RONTGEN RAYS IN GASES AND VAPOURS. 



271 



blast method was employed in the measurement of the mobilities. The following 
results are given in PRZIBRAM'S paper : 



Vapour. 


- * + . 


k-. 


Temperature. 


Water 


cm. /sec. 
0-77 


cm. /tee. 

0-73 


C. 
100 


Methyl alcohol .... 


0-29 


0-30 


66 


Ethyl alcohol 


0-26 


0-27 


79 


Benzol 


0-18 


0-21 


80 


Aceton 
Chloroform 
Hexane . . . 


0-11 
0-19 
0-15 


0-12 
0-16 
0-16 


57 
58 
69 


Ethyl ether 


0-15 


0-16 


35 


Methyl acetate 


0-14 


0-18 


58 



111 the cases of ethyl alcohol, aceton, ethyl ether, and methyl acetate, it is noticeable 
that the mobilities are much smaller than when measured at pressures well removed 
from the saturated state and reduced to a pressure of 760 mm. of mercury in 
accordance with the law pk = constant. It is probable that in the case of every 
vapour, just as has been shown in the particular case of ethyl chloride, the values of 
pk would decrease if pressures were chosen so as to make the vapour approach 
saturation. As an analogous illustration of this point, it is worthy of mention that 
PHILLIPS* has shown that the ionic mobilities when measured in air at atmospheric 
pressure vary as the absolute temperature over a wide range of temperatures ; but, 
in the neighbourhood of the temperature of boiling liquid air, the mobilities are 
distinctly smaller than would be the case if this law of variation were applicable. 

A preliminary examination of the results which are given in Tables I. and II. shows 
that there is no direct dependence of the 1 ionic mobility on the molecular weight ; it 
might have been expected that the mobilities would decrease as the molecular weight 
increased, but that this is not always true is seen by comparing the cases of ammonia 
(molecular weight 17 and mean ionic mobility - 77 cm./sec.) and oxygen (molecular 
weight 32 and mean mobility 1'58 cm./sec.). A better way of considering the results 
would be to divide the list into two groups, placing in one group those gases which 
have a relatively small critical temperature, and in the other those (the so-called 
vapours) which have a relatively high critical temperature ; it will then be seen that 
the high mobilities belong without exception to the gases of the first group ; the 
apparently small values of the ionic mobilities in certain cases, e.g. ammonia and 
aldehyde, can then be conceived as being due to large cohesive forces between their 
molecules evinced by their relatively high critical temperatures. An attempt to 
deduce the mobility values from purely theoretical considerations is given later under 
section 9. 

It is noticeable also from an inspection of the tables that, especially in the case of 

* 'Roy. Soc. Proc.,' A, vol. 78, p. 167, 1906. 



272 MR. E. M. WELLISCH ON THE MOBILITIES OF THE 

vapours, there is little difference in value between the positive and negative 
mobilities. The greatest differences are found for the elementary gases : air, oxygen, 
hydrogen, and helium. There are several instances, including most of the ethyl 
compounds, in which the positive ion has a greater mobility than the negative; 
hitherto, only one gas, viz., acetylene,* was known in which this was the case. 

9. Theoretical Considerations. 

The Law of Mobility of the Ions formed in Gaseous Media. In the following 
treatment, which is based on the kinetic theory of gases, an attempt is made to obtain 
a theoretical expression for the velocity with which a charged body of dimensions 
comparable with those of a molecule would move in the gas under the action of an 
electric field of given intensity. It is necessary at the outset to fix our ideas of a 
molecule and an ion ; for this purpose the following conceptions are introduced : 

A molecule is regarded as a nucleus surrounded by a sphere of force of radius ^s. 
The spheres of force are supposed mutually impenetrable. 

An ion is regarded as involving two distinct elements : 

(i) A mass (independent of the charge). Considering this element alone, let us 
represent the ion as a nucleus surrounded by a sphere of force of radius ^s'. 

(ii) A charge e (electrostatic units). During motion of the ion through the gas 
the effect of this charge is equivalent (as will be shown) to an increase in the volume 
of the force sphere (i) of the ion, the mass remaining unaltered. 

A collision occurs between two molecules when the distance between their centres 
is equal to the sum of the radii of their force spheres. 

LANGEVINJ has shown that the velocity of an ion under unit electrostatic intensity 

is given by 

k = eL/MV, 

where M denotes the mass of the ion, L its mean free path through the gas, and V its 
mean velocity of thermal agitation. As the ion moves through the gas the charge 
associated with it attracts the neutral molecules ; there results an increase in the 
mean collision frequency of the ion and consequently a diminution in its mean 
free path. 

Expression for the Mean Free Path of the Ion. Consider the motion of an ion and 
a molecule regarded in the light of two interacting free particles. Let E, denote the 
potential due to the polarisation of the molecule by the charge on the ion,! so that the 

* ZELENY, 'Phil. Mag.,' vol. 46, p. 132, 1898. 
t 'Ann. de Chim. et de Phys.,' vii., 28, p. 335, 1903. 

I The polarisation of the molecule by the electric field is regarded as negligible in comparison with that 
due to the ionic charge. 



IONS PEODUCED BY RONTGEN RAYS IN GASES AND VAPOURS. 273 

force, taken as wholly radial, between the ion and the molecule is given by dR/dr at 
a distance r. Let us reduce the molecule to rest and consider the relative motion as 
the ion approaches it so that the velocity at infinity was U. The interacting forces 

must now be considered as being derived from a potential ]F^f3&fn denoting the 

/**** /yq 
mass of the molecule. X*s4&*^ 

The shortest distance r to which the ion and the molecule approach is given by 

the equations 

= ru, 



m 



where u denotes the velocity of the ion in this position and b is the length of the 
perpendicular from the molecule to the rectilineal path of the ion. 
We deduce 



A collision will take place if 



where cr = ^s' + ^s, the sum of the radii of the force spheres of the ion and molecule, 
and 11, denotes the value of E, at collision. 

If R = 0, i.e., if the polarisation of the molecule due to the ionic charge is negligible, 
the condition for a collision reduces to b S cr, as is otherwise obvious. 

The connection between the velocity U and the mean thermal ionic velocity V can 
be deduced by the application of MAXWELL'S law of distribution of velocities. We 
obtain 

U 2 = VU+ N 
m 



Hence A ^- U 2 = AMV 2 = mv 2 ; thus A -- U 2 is the mean kinetic energy of 
2 M + m 2 M + m 

the molecular motion. 

The effect of the polarisation due to the ionic charge is, therefore, as far as collisions 
are concerned, to replace <r 2 by cr 2 {1 + 2R <7 /mv 2 }. 

Now the mean free path of an uncharged body of the same mass and dimensions as 
the ion is given by {ira<r 8 \/l + M/m}~ 1 , where n denotes the number of molecules per 
cubic centimetre. Hence the actual mean free path of the ion is L, where 



VOL. ccix. A. 2 N 



274 MR. E. M. WELLISCH ON THE MOBILITIES OF THE 

Expression for the Potential R due to the Polarisation of the Molecule by the Ionic 
Charge. If the molecules of a gas are polarised by an electric field of intensity X, 

XT' _ 1 

the electric moment per cubic centimetre is - X, where K denotes the dielectric 

4?r 

jr _ i 

constant of the gas. The electric moment (u.) of a molecule is therefore - X. 

47m 

The mechanical force 011 the molecule is u -= , which is equal to -- = . The 

dr 8im dr 

potential is therefore given by 

R = ~ ~ 



- 
8Trn 8-irn ' r 4 ' 

when the molecule is polarised by the field due to the ionic charge. 

This expression for R assumes that the polarising field is uniform throughout the 
volume of the molecule. L ANGEVIN (loc. cit., p. 317) has obtained the general 
expression for R in the case of a spherical molecule and finds it to be given by a series 
of which the above is the most important term. 

Expression for the Mobility of the Ion. Let 17 denote the coefficient of viscosity of 
the gas, p its density, p the pressure in dynes per square centimetre, and I the 
molecular . mean free path. Let n 1; p 1} p lt Kj denote the values of n, p, p, K respec- 
tively corresponding to a temperature of C. and a pressure of 760 mm. of mercury. 

The charge e carried by the ion is taken as equal to that (E) on the monovalent 
ion in the electrolysis of solutions. This equality was established from measurements 
of the mobility and rate of diffusion of gaseous ions.* The exact value of the ionic 
charge is not required in the present treatment, inasmuch as e only enters in the 
expression n^e = WjE, which has been shown from experiments in electrolysis to have 
the value l'30x!0 10 ,t E being measured in electrostatic units. The product n t E is 
denoted by A. 

The gas is regarded throughout as being at a temperature of C. 

We have the following equations : 

k = eL/MV, 77 = 

I- 1 = Tr\/2ns\ 



m mv 



where <r = 



Srm 



MV 2 = mv 2 (equipartition of energy), 
e = E, p = nm, 

jE = A, p = 



* Fide J. J. THOMSON, ' Conduction of Electricity through Gases,' 2nd edition, Art. 39. 
t The electro-chemical equivalent of hydrogen was taken as - 00001035 gram/coulomb. 



IONS PRODUCED BY RONTGEN RAYS IN GASES AND VAPOURS. 275 

We deduce the expression for the mobility in the form : 

AT? /-/mY' 3 /! .MY- 1 */. . V 8 J . 4(K-l)e 2 

'- -- ~ -- -- 



T? /-m! .. . . -e 

= '- 4\/2 hey 1H -- 1 + ~ lH -- jT7 -- mf 

l \M/ \ m/ \ */ I 7mmv 2 s+s') J 



When the mass and dimensions of the ion are the same as those of a molecule, we 
have M = m, s' = s, and the expression for the mobility becomes 



This expression can be transformed into 

(J 



Consider the expression (a) which has been found for the velocity of an ion, 
regarded as a molecule carrying a charge equal to that associated with the monovalent 
ion in electrolysis, moving under unit electric intensity in a gaseous medium at a 
pressure p dynes per square centimetre and a temperature of C. 

For a given medium K^, p lf and p^ are constant ; whence k varies inversely as p, 
provided ? is constant. Now, by MAXWELL'S law,* the coefficient of viscosity of a 
gas is independent of its density ; consequently over the range of pressures for which 
this law holds good we should expect the ionic mobility to vary inversely as the 
pressure, a conclusion which has been verified experimentally. 

The expression (a) involves only known physical constants of the gas and is 
therefore directly comparable with the results of experimental observation. The 
results obtained by substituting the observed experimental values of the quantities 
involved are given in Table III. The values of the viscosity coefficients and of the 
dielectric constants have been taken from LANDOLT and BORNSTEIN'S Tables (3rd 
edition) ; the constant p l was taken as 1,013,610 (dynes per square centimetre). 

The sixth column in the table affords an indication of the effect on the mobility of 
the electric polarisation of the molecules due to the ionic charge ; it will be seen that 
the effect is quite considerable. Column seven gives the values of the mobilities 
under a potential gradient of 1 volt per centimetre, which would be possessed by a 
molecule carrying a charge E if there were no retarding effect due to this polarisation. 
The remaining columns give the values of the mobilities as deduced from the 
expression (a) together with the observed experimental values of the positive and 
negative ionic mobilities ; these values correspond to. a real or hypothetical pressure 
of 760 mm. of mercury. 

Unfortunately the values of K have been determined experimentally for only a 
very limited number of gases and vapours ; in consequence, several vapours whose 
mobilities have been ascertained do not appear in the table. 

* Vide JEANS, ' Dynamical Theory of Gases,' p. 252. 
2 N 2 



276 



MR. E. M. WELLISCH ON THE MOBILITIES OP THE 
TABLE III. 



1. 


2. 


! 

3. 4. 


5. 


6. 


7. 


8. 


9. 


10. ' 
















two- 


Gas or 
vapour. 


Molecular 
weight. 


PI x 10*. 


ij x 10. 


(K! - 1) x 10-''. 


(K!-l)rAV 


**"(WP} 


Cal- 


Observed. 


2piVi 
















culated. 


* 


- 


Air 




129 


177 


59 


3-70 


5-87 


cm. /sec. 
1-25 


cm. /sec. 

1-36 


cm. /sec. 

1-87 


Ho 


2 9 85 26 5-39 40-38 6-32 


6-70 7-95 


CO 


28 


125 163 69 3-79 5-58 1-16 


1-10 1-14 


N, 


28 


125 163 59 3-24 5-58 1-31 


1-6* 


O 2 


32 


143 191 54 3-56 5-71 1-25 


1-36 


1-80 


CO 2 


44 


196 141 96 


2-52 3-07 0-87 


0-81 


0-85 


N 2 


44 


196 141 


107 2-80 3-07 0-81 


0-82 : 0-90 


NH 8 


17 


76 96 


770 24-13 5-40 0-21 


0-74 0-80 


C 2 H 


46 205 83 


940 S-16 1-73 0-19 


0-34 0-27 


C,H 5 C1 


64-5 


288 93 1554 12-06 1-38 0-11 


0-33 


0-31 


C 4 H 10 


' 74-1 


330 69 742 2-77 0-89 0-24 


0-29 


0-31 


ecu 


153-8 


686 


153 


426 


3-76 0-96 0-20 


0-30 0-31 

1 



* Mean value. 

Considering that we are comparing the observed values of the mobility with absolute 
values calculated from various physical constants of the substances, the agreement is 
in several cases quite satisfactory ; however, in the case of ammonia and the vapours 
there is a marked divergence between the calculated and observed values, the former 
being invariably smaller. The values of the dielectric constants for the vapours 
appear to be inordinately large, and, in this connection, it is interesting to note that 
it is also in the case of vapours that there is a marked departure from MAXWELL'S 
law, K = n 2 , where n is the refractive index. The following table will serve as an 

illustration : 

TABLE IV. 



Gas or vapour. 


K. 


K 1 ". 


. 


Air 
H 2 
CO 
C0 2 

N 2 


1-Q00590 
1-000264 
1-000690 
1-000960 
1-001070 


1-000295 
1-000132 
1-000345 
1-000480 
1-000535 


1-000294 
1-000138 
1-000340 
1-000450 
1-000500 


NH 3 
C 2 H 6 
C 2 H 6 C1 


1-0077 
1-0094 
1-0155 


1-0038 
1-0047 
1-0077 


1-00037 
1-00086 
1-0010 



IONS PRODUCED BY RONTGEN RAYS IN GASES AND VAPOURS. 277 

In the case of MAXWELL'S law the reason for the departures is probably the 
existence in the molecule of free periods with durations long compared with that of 
the incident wave period.* It is possible that, in the case under consideration, owing 
to free periods of long duration in the molecules of the vapours, these have not time 
to be completely polarised by the adjacent ionic charge during a collision. It is 
worthy of mention that the large values of K which have been experimentally 
obtained for ammonia and vapours have been ascribed by some authorities! as being 
partially due to traces of conductivity which they possess. 

Without dwelling further on the cause of these departures from the mobility law, 
it appears that, on the whole, the experimental values of the mobilities of the ions 
can be explained approximately on the supposition that the ion consists of a single 
molecule of the gas with which is associated a charge equal to that carried by the 
monovalent ion in electrolysis. It has been shown from considerations based on the 
kinetic theory of gases that, irrespective of any theory as to the structure of the ion, 
the ascertained mobility values lead of necessity to the conclusion that the volume of 
the ion is in all cases greater than that of the corresponding gaseous molecule. The 
question arises : what is the nature of this volume ? On the one hand, if we neglect 
the influence of the charge on the mean free path of the ion, we are led to the 
conception of the ion as a cluster of molecules held together by forces arising from the 
polarisation due to the electric charge. On the other hand, the effect of the charge 
on the collision frequency has been shown to be equivalent to an increase in the 
molecular sphere of force such that the resultant effective volume is sufficient to 
explain approximately the observed mobilities. On this view the effect of the charge 
is to cause the ion itself and the neighbouring molecules to deviate from their rectilineal 
free paths ; SUTHERLAND,^ by assuming such deviations to occur in the case of gaseous 
molecules by reason of attractive forces between them, was able to explain accurately 
the observed variation of the viscosity of gases with temperature. LANGEVIN has 
obtained an expression for the ionic mobility by using the dynamical method employed 
by MAXWELL in the kinetic theory of gases ; he concluded that the experimental 
values of the mobilities lead to the necessity of regarding the ion as a cluster of 
molecules. The question as to the nature of the volume of the ion as determined 

st 

from the experimental mobility values could be decided if the ratios for the 

different gaseous ions were known. In this connection it is worthy of mention that 
Prof. Sir J. J. THOMSON || has recently measured this ratio for the positive ions formed 
by cathode particles in oxygen at low pressures and came to the conclusion that the 
ion consisted of a single charged oxygen molecule. 

* Fide DRUDE, ' Theory of Optics,' Eng. trans., p. 389. 

t Fide BADEKER, 'Zeits. Phys. Chem.,' Bd. 36, p. 321, 1901. 

t 'Phil. Mag.,' vol. 36, p. 507, 1893. 

' Ann. de Chim. et de Phys.,' vol. 5, p. 284, 1905. 

|| 'Phil. Mag.,' vol. 16, p. 680, 1908. 



278 ME. E. M. WELLISCH ON THE MOBILITIES OF THE 

Mention has already been made (vide section 8) of the increase in value of the 
product pk at low pressures in the case of air, nitrous oxide and carbon dioxide, and 
of the diminution in the case of vapours, e.g. ethyl chloride, when the pressures 
approach the vapour pressure at the temperature under consideration. Such 
deviations from the law pk = constant could be ascribed to variations in the size 
of the cluster constituting the ion ; however, they follow readily from the expression 
(a) of the mobility if we take into account the deviation from the law of MAXWELL 
which states that the coefficient of viscosity of a gas or vapour is independent of its 
density. In the case of gases it is known that 77 diminishes as the pressure is reduced 
beyond a certain value;* such a diminution would, according to the theory here 
given, produce an increase in the value of pk. In the case of vapours it has been 
established that r/ increases rapidly as the saturated state is approached ; in fact, as a 
result of WARBURG and VON BABO'S experiments on the viscosity of CO 2 at high 
pressures. MEYER! came to the conclusion that the experimental values above certain 
pressures could be explained only by supposing carbon dioxide to behave as a liquid, 
the density of which is practically independent of pressure ; an increase in the value 
of 77 would, according to the expression (a), diminish the product pk, a result in 
accordance with experimental observations. 

10. Summary. 

1 . The velocities of the positive and negative ions produced by Rontgen rays in 
4 gases and 15 vapours have been measured at normal temperatures over a wide 
range of pressures and under different electric intensities. LANGEVIN'S null method 
was employed throughout. 

2. For a constant pressure the velocity of the ion was found to vary as the electric 
intensity. 

3. It was found that, in general, the mobility (k) of the ion varied inversely as the 
pressure (p). In the case of nitrous oxide and carbon dioxide there was a slight 
increase in value of the product pk both for the positive and negative ions as the 
pressure was reduced below about 7 cm. of mercury. In the case of ethyl chloride 
there was a marked decrease in the value of pk as the vapour approached the 
saturated state ; there is reason to believe that such a diminution would appear in 
the case of all the vapours in the neighbourhood of the saturated state. 

4. In the case of vapours there was, in general, little difference in the values of 
the positive and negative mobilities. The mobility of the positive ion was found 
greater than that of the negative for aldehyde, ethyl alcohol, -aceton, sulphur dioxide, 
ethyl chloride, pentane, ethyl acetate, methyl bromide, and ethyl iodide. 

5. There appeared to be no direct relation between mobilities and molecular 

* Vide JEANS, loc. tit., p. 253. 
t Loc. tit., Art. 90. 



IONS PRODUCED BY RONTGEN RAYS IN GASES AND VAPOURS. 279 

weights ; the smaller mobilities invariably belonged to gases possessing high critical 
temperatures (the vapours) ; the larger mobilities to gases with low critical tempe- 
ratures. 

6. From the kinetic theory of gases an expression has been deduced for the 
mobility of an ion moving through a gaseous medium under the influence of an 
electric field. This expression takes into account the effect of the charge carried by 
the ion on its mean free path and involves only known physical constants of the gas. 

7. As a result of the theoretical considerations it appears that the experimental 
values of the mobilities in the different gases at various pressures, as well as certain 
observed deviations from the law connecting the mobility and gaseous pressure, can 
be explained approximately on the supposition that the ion consists of a single 
molecule with which is associated a charge equal to that carried by the monovaleut 
ion in electrolysis. 

I take this opportunity of expressing my indebtedness to Mr. H. C. WILSON for 
setting up part of the apparatus ; in conclusion, my thanks are due to Prof. THOMSON 
for the generous interest he has manifested in the research and to Prof. LARMOR for 
helpful advice. 



[ 281 J 



XII. Determination of the Surface-Tension of Water by the Method of 

Jet Vibration.* 

By N. BOHR, Copenhagen. 

Communicated by Sir WILLIAM RAMSAY, K.C.B., F.R.8. 
Received January 12, Read January 21, 1909. 

Introduction. 

IT has been shown that one of the most important and difficult questions in regard to 
the determination of the surface-tension of water is to produce a sufficiently pure 
surface, and in later investigations great importance has therefore been attached to 
this point. 

In 1879 Lord RAYLEIGH, t however, indicated a method which solves the above- 
mentioned difficulty in a far more perfect manner than any other method used 
hitherto ; this method makes it possible to determine the surface-tension of an almost 
perfectly fresh and constantly newly formed surface. 

In the paper cited above, Lord RAYLEIGH has developed the theory of the vibrations 
of a jet of liquid under the influence of surface-tension, and as appears from this 
theory, it is possible to determine the surface-tension of a liquid when the velocity 
and cross-section of a jet of liquid, and the length of the waves formed on the jet, 
are known. 

Lord RAYLEIGH has attached a series of experiments to the theoretical development. 
By these experiments, however, it was more especially intended to give illustrations 
of the theory rather than to give an exact determination of the surface-tension. 

If, however, this is the problem, it is necessary to consider more closely some 
questions which are not discussed in Lord RAYLEIGH'S investigation, for it is necessary 

* Based on a response to Det Kongl. Danske Videnskabernes Selskabs (The Royal Danish Scientific 
Society's) Problem in Physics for 1905; delivered October 30, 1906; awarded the Society's Gold Medal. 
(The investigation has since been completed with a number of experiments.) 

t Lord RAYLEIGH, 'Roy. Soc. Proc.,' vol. XXIX., p. 71, 1879. 

VOL. CCIX. A 452. 2 O 25.5.09 



282 MR N. BOHR ON THE DETERMINATION OF THE 

to be sure, first, that the theoretical treatment is sufficiently developed, and secondly, 
that the phenomenon satisfies, to a sufficient degree, the assumptions on which the 
theoretical treatment rests. 

The main purpose of the present investigation is to try to show how this can 
be done. 

In spite of the great advantages of the above-mentioned method for the deter- 
mination of surface-tension, it has, however, not been very much used. Except by 
Lord RAYLEIGH,* the method has till recently been used only by F. PiccARDt and 
G. MEYER| for relative measurements. During the completion of this investigation a 
treatise on this subject has been published by P. O. PEDERSEN. 

The Theory of the Vibration* of a Jet. 

The theory of the vibrations of a jet of liquid about its cylindrical form of equilibrium 
has been developed by Lord RAYLEIGH for the case in which the amplitudes of the 
vibrations are infinitely small and the liquid has no viscosity. 

The equations found by Lord RAYLEIGH can, when the amplitudes have small 
values and the viscosity coefficient is small, be considered as a good approximation ; 
but if the equations are to be used for exact determination of the surface-tension, it is 
of importance to know how great the approximation is under the given circumstances. 
In the first part of this investigation we will therefore attempt to supplement the 
theory with corrections both for the influence of the finite amplitudes and for the 
viscosity. 



Calculation of the Effect of the Viscosity. 



Under the influence of the viscosity the jet will execute damped vibrations. If 
the problem is to find the law according to which the amplitudes decrease, this can, 
when the viscosity-coefficient is small, be done with approximation by a simple 
consideration of the energy dissipated. Some authors || are of opinion that the 
correction on the wave-length (time of vibration) due to the viscosity for a problem of 
this kind can be found directly from the logarithmic decrement of the wave- 
amplitudes 8 by means of the formula Tj = T (l + S 2 /47r 2 ) 1/2 , where T! is the time of 
vibration with damping, T is the time of vibration without it. This application of the 
formula given does not, however, seem to me to be correct. For the formula is 
established for a problem by which the only difference between the equation of motion 

* RAYLEIGH, ' Roy. Soc. Proc.,' vol. XLVIL, p. 281, 1890. 
t PiCCARD, 'Archives d. Sc. Phys. et Nat.' (3), XXIV., p. 561, 1890 .(Geneve). 
J MEYER, ' WIED. Ann.,' LXVL, p. 523, 1898. 
PEDERSEN, 'Phil. Trans. Roy, Soc.,' A, 207, p. 341, 1907. 

|| P. 0. PEDERSEN (loc. cit., p. 346) ; and PH. LENARD (' WIED. Ann.,' XXX., p. 239, 1887) in his paper 
about the analogous problem, the vibrations of a drop. 



SURFACE-TENSION OF WATER BY THE METHOD OF JET VIBRATION. 283 

(^\ 2 
a ^L + C q = 0. One degree ot 
Gv 

freedom. Small oscillations. Free motion I and the equation of motion for the 

dissipative system consists in the addition of a frictional term ( a -% + b-^ + cq = 

\ dt 2 tit 



In the present pi-oblem as in all fluid-problems in which a velocity-potential exists 
for the conservative system, but not for the dissipative one the coefficient of inertia a 
will not be the same for the two systems, since a in the dissipative system is dependent 
on the coefficient of viscosity. 

As will be seen from what follows, the correction on the wave-length will not be 
proportional to S 2 but to 8 :V3 . 

In order to find the variation of the wave-length due to the viscosity, the problem 
"must be treated in greater detail. Such an investigation is given by Lord RAY LEIGH* 
for the vibrations of a cylinder of viscous fluid under capillary force, in the case where 
the original symmetry about the axis of the cylinder is maintained. In the develop- 
ment to be found in the paper cited above, the assumption mentioned (the symmetry) 
is, however, from the outset used in such a manner -that the calculation cannot be 
extended to treat the more general vibrations which will be mentioned here. The 
result of our development does not include the problem investigated by Lord RAYLEIGH, 
as, in order to simplify the calculation, special precautions relative to the limiting case 
(n = 0) are not taken. 

The general equations of motion of an incompressible viscous fluid, unaffected by 
extraneous forces, are 



and 



in which u, v, w are the components of the velocity, p the pressure, p the density, 
ju, the coefficient of viscosity, and 

v = + J*L + f*l *L ~ ?. M A r jl w l 

In the problem in question the motion will be steady. Putting w = c + w, and 
supposing that u, v, and w have the form f(x, y) e^ z , and that u, v, and o> are so small 
that products of them and quantities of the same order of magnitude can be neglected 
in the calculations, we get from the equations (1) 

- 19 P. /ai 



T7 */i ' 1 Ir i T7 '/ r \ 



* Lord RAYLEIGH, 'Phil. Mag.,' XXXIV., p. 145, 1892. 
2 o 2 



284 MR. N. BOHR ON THE DETERMINATION OP THE 

from (3) and (2) it follows that 

Vp = ............ (4) 

Putting 

i 3 i 3x> i dp , / c \ 

u = -r-^-+u l , v = ^-^+v l} a> = - r ^+<a l .... (5) 
cbp fix cbp dy cop tiz 

we get 

(V-t&^w^O, (v-ib^v^O, (V-ib^w^O, ... (6) 

It I p-J 

and 



3z 



Now introducing polar co-ordinates r and (.-r = / cos &,y = r sin 3), and the radial 
and tangential velocity a and /3, we get, by help of the following relations, 

3 ^ 1 ^ 

a = a cos .5 /3 sin , (^ = a, cos ^ R sin 3, ^ = cos ^ - -- sin 5 - ^-, 

ex or r dy . . 

1^ 

1 ^ -i j\ 

v = a sin S + B cos 5, '! = aj sin -9 + /3j cos , ^- = sin -5^- + cos 3 - ^-, 

o?y o?' T o-t 

from (5) 

....... (9) 



p\2 i o 1 r) 2 J5 2 

and from (6) and (7), considering V = ^ + - ^- + - 2 ^ + ^, 



and 

3o 1 a i l3 J 8 1 3a. 1= 



Now supposing that p, a, ft, <a, and consequently a u /S^ &)i, have the form 
/(r)e"'* + ''*-', we get from (4) 



of which the solution, subject to the condition to be imposed when r = 0, is 

......... (12) 






in which J n is the symbol of the BESSEL'S function of rt th order. 
From (6) we get 



which gives 

. . . . (14) 



SURFACE-TENSION OF WATER BY THE METHOD OF JET VIBRATION. 285 
Eliminating & from (10) and (11), we get 

/ -r C0\ . 3! . i 3o>i 

r V-tD -<! + 2-^ + ' = -2-^, 
\ /* / or r 02 

which gives 



(15) 
/ 

We have, however, 



whence we get 

J.J.(ar)i* l + * r l = 2/ f 6'+ASe > )j.(Wr)^ l *** i = 2#J ll (id/-)e" s+a *; (16) 
or J p./ 

from (15) and (16) we get 

a l =^W n (id r )+C3 n (ich')^e<>+*, ...... (17) 

and from (11) we get 

1 3/8! _ 3aj , i , 3d)! 
r 35 3r r 3z 



e"'* + *-". . (18) 

With the help of the relation 

J.() + ij + (l-5)j.()-0 ...... (19) 

U./ \ tX/ / 

(18) gives 

(20) 



Introducing in the equations (9) and (5) the values of p, a. l} fi lt and aj 1( found by 
(12), (14), (17), and (20), we get 



a = - 



JB BB ^^, . . . (21) 

bcp r a r 



= c+[ -A 



286 MR. N. BOHR ON THE DETERMINATION OF THE 

Let us suppose that the equation of the surface is 

r-a = = De" s+d ". 
The general surface-condition gives 

D , /a/33 a \, n 

(r-a-Q = -.+ e- +w -(r-a-Q = 0, 



whence we get, neglecting quantities of the same order of magnitude as above, 

- !- l = ~lk" ......... < 22) 

In the same manner we get further, if the principal radii of curvature are Rj 
and R 2 , 

J_ J_ 1 L 1^_^ 1 i(n'-l + yq') (23 . 

ft, K 2 a 2 2 as 2 W ~ <t a 2 cb 

Let Pr, PS, Pz be respectively the radial, tangential, and axial component of the 
traction, per unit area, exerted by the viscous fluid across a surface-element 
perpendicular to radius-vector. Taking the radius-vector concerned as X-axis, and 
using the notation generally employed, we have 

D du T3-, /dv , ou\ -rj idw , 'du 

pr-.= P ^= - P+ ^-, P^ = ^,.V = /^^+^J> n -A--/*^ + 

Using the relations (8), and after the differentiation setting & = 0, we get 

a dw\ ,.% 

+ _. . (24 ) 



Calling the surface-tension T and assuming that there is no " superficial viscosity," 
the dynamical surface-conditions will be, using the same rate of approximation as 
before, 

+ ^Wpr = const., PS = 0, Pz = ; ..... (25) 



.;_:> 

(26) 



from (25) we get, using (23) and (24), 



a 3_A = /a. |px =a -- } 

r 8^ 8r r/,- = \3z or/,- = a 

Introducing in these conditions the values of p, a, y8, w found by (12) and (21), we 
get, after the elimination of B/A and C/A, an equation for the determination of 6. 



SURFACE-TENSION OF WATER BY THE METHOD OF JET VIBRATION. 287 

As these calculations will be rather long and the result unmanageable, we will not 
perform the elimination exactly, but only with an approximation which takes regard 
of the application of the results. 

In the experiments the numerical value of iab will be small the wave-length 
large in comparison to the diameter of the jet and the numerical value of iad 
great the coefficient of viscosity small (in all the experiments |w&|<0'24 and 
| iad \ > 20). 

For every value of x we have 



x" 



2 B [n] 2 B+ 

The series converges rapidly for small numerical values of x, but very slowly for 
great values. From (28) it follows that 



T' / \ _ '"- T / \ 1 . 

= x ~ 

and further, by (19), that 



i) _ EL _ 1 

n + 1 ) + 2>^iy^Tl)>+2) ' ' ' J ' 



'2 (n- 1 ) ( 

Referring to the above, by the calculation of the frictimial terms in the equation 
for the determination of b, we will therefore put 



in T / / \ f f* 2 & 2 

= -- = J B (M) 1 + 7 -7 
ab '\_ 2n(n+ 







For calculating J n (x) for great values of x the asymptotical expression 

., J n (x)^(2vx)->{[P n (x) + iQ(x)]e(*-^+[P n (x)^^^ . (30) 

is used, in which 

, , _ (4n a -l 2 )(4n 2 -3 2 ) (4>^-l 2 ) (4 ft 2 -3 2 ) (4n 2 - 
1.2(8^) 2 1.2.3.4 (8a,-) 4 

and 

Q M _ (4n 2 -! 2 ) (4n 2 - 



1.2.3(8o;) 3 






A few terms of the formula (30), which is only correct when the real component 
of x is positive, will for a great numerical value of x give an excellent approximation 
for J B (x). By our application of the formula (30), x can be given the form aib, 



288 MR. N. BOHR ON THE DETERMINATION OF THE 

where both a and b are great positive quantities. Thereby the term with e lz will 
be quite predominant ; we therefore get, neglecting the term with e~", 

and further, by (19), 

J" B (.r) = -J.(a 



In the following calculations we will therefore put 

aud J.(M) = + J.<rf)l + + . (31) 



From (27) we get now, using (29) and (31), 

23 



+ 2 + ^l) = 0, . (32) 
n \ ad a,dr ] 

and 

-CJ.(rf) = ; (33) 



12ri 2 -8n-3 



from (32) and (33) we get 

* IT/ ;\2fi 2 ^ 2 

= ^A J B (*a6) 7 1 + 7 

cp ' ad\_ 2w(n+l 



and . (34) 

nT/ . JX A IT/- t\*2 3 (-l)ri , 2 ^ 2 Vi 2 2w 3 -3\ 

CJ n (^af^) = -^-A J B (t6) -- i-js ' 1 + / 2 T\ I 1 -- j -- O5~ 
cp 2 a a o L 2(r 1)J\ ad a'a? I 

From (26) we get now, using (12), (21), (29), (31), (34) and (13), 

V-ibH: M!izl). n + <M_\ \ l + ^ + (!^(^- 8 )1 
p a?c L n(nl)j L ^ 2a a cP J 

8 ) = 0. . (35) 



Putting p. = in (35), we get the solution of Lord RAYLEIGH,* 

A 2 T ta "oJ n( ^CT ^o) / 2 l , ,,27, 8\ 

V 2 a 3 J n (M,) ( 

T(n'-n)f (3n-l)aV 3(n+3)V 1 

pcV L 2n(n 2 -l) 8n(n-l) (n+1) 2 (n + 2) "J" 

In the following we wilt denote the positive root of this equation by &. 
* Lord RAYLEIGH, 'Roy. Soc. Proc.,' vol. XXIX., p. 94, 1879. 



SURFACE-TENSION OF WATER BY THE METHOD OF JET VIBRATION. 289 
From (35) and (36) we get, with the same approximation as used hitherto, 



p ac 
With the same approximation it will be permissible, by use of (13), to put in (37) 

cp\ 1 ' 2 ,, .,fa 2 k 
-\ =l-i- 2 



choosing the sign for iad so that the real component is positive [see (30)]. 
The equation (37) now becomes 






2n(n'-l) 

. v .o. . (38) 



2 \ pea 2 Ay 4 \pca 2 & 

Now solving (38) with regard to b, and setting /; = k + ie, we get 

--* fl - M (- 1 )Y ^ Y /3 3*(*-l)V 2 ^ VI 

"T~ "Ipca^y 4 "v^o^y J 



and 

n-l 



_ 
" 



, - ^ , , 

2 - 



As all the equations used are linear, it will be seen that the physical meaning of 
the above calculation is the proof of the existence of a real fluid-motion corresponding 
to a surface of the form 

r = a + be~" cos kz cos n$, 

where k and e are expressed by the equations (39) and (40). 

The correction, which on account of the effect of the viscosity is to be introduced in 
the expression for the surface-tension, can be found by (36) and (39) ; we get 



3/3 , 3n(n-l)V ' 
- i '- 



\ 2 ~| 

. . (41) 
/ J 



- - y 
\pca 2 kj 2 \pca 2 k 

Calculation of the Influence of the Finite Wave-amplitudes. 

We will now calculate the correction of the wave-length due to the magnitude of 
the wave-amplitudes. The method of approximation which will be used is on the 
principle indicated by G. G. STOKES.* 

The following calculation will only treat of the vibrations in two dimensions of a 
fluid-cylinder without viscosity. The problem in three dimensions could be treated 

* G. G. STOKES, ' Camb. Trans.,' VIII., p. 441, 1847. 
VOL. COIX. A. 2 P 



290 ME. N. BOHE ON THE DETEEMINATION OF THE 

in a corresponding manner ; but the calculations would in this case be very extensive, 
and, with regard to the present investigation, it would not be of any practical 
importance. Using jets the diameter of which is small in proportion to the wave- 
length, the motion will differ so little from the motion in two dimensions that the 
small correction of the wave-length due to the finite values of the amplitudes can be 
considered the same in both cases. 

In the present problem the existence of a velocity-potential < can be supposed. 
Using polar co-ordinates and calling the radial and tangential velocity respectively a 
and |8, we get 



Considering the fluid as incompressible, we get 



" Zr r r 8S ~ \3r 2 r Sr r 2 

The solution of (l), subject to the condition that the velocity shall be finite for 
r = 0, can be written (n being a positive integer) 



)sin(^ + e, 7 ) ........ (2) 

The equation of the surface can be written 



The surface-conditions are, using the same notations as above and calling the radius 
of curvature of the surface R, 



From (3) we get 

1 ^b ^ w y ^b , ^y \ _ A 

r\ . f> ~f\ n f\ n I ^\ / 

and 



P 1 g^ 2 I i a-v. / Ijl 2o 



=0. . (5) 

Considering only small vibrations of the surface about the position of equilibrium 
r = a, is a small quantity which we will consider as being of the first order. From 
(2), (4), and (5) it can be seen that <f> must also be of the first order, when F (t) is 
defined in such a manner that < does not contain terms independent of r or 5. 



SURFACE-TENSION OF WATER BY THE METHOD OF JET VIBRATION. 291 
From the equations (4) and (5) we get, by help of TAYLOR'S theorem, 



* 3r 2 8r 

and 



[ 






From (2), (6), and (7) can be found except for a constant, which can be determined 
by the condition 

f2ir ra + f f2.r 

rdrd$=\ ^(a + WdS- = ira* ....... (8) 

Jo Ju Jo 

First Approximation. 

(Solution of the problem neglecting all terms of higher order than the first.) 
From (G) and (7) we get 



and 

M _ T 

a a 
Eliminating from (9) and (10), we get 

+F(I)-0 ....... (11) 



Putting F() = 0, (11) will be satisfied by 

T 
$ = A? 1 " cos n3 sin gi when q 2 = s (n 8 n) ..... (12) 

DC' 

Introducing this in (9), we get 

P = -wcT^A cos n sin o, C = - o-^A cos nS cosg<+/(^). . . (13) 
ct q 

From (10) we get, using (12) and (13), 

" (.) = const, 



which is satisfied by 

/() - C- 
From (8) we get in this case 

= 0. 

2 P 2 



292 ME. N. BOHE ON THE DETERMINATION OF THE 

To a first approximation we get as the general form of the vibrations 



r 



cos 



cos 



where q n 3 = - 3 (n 3 n). 
oct 



As to the higher approximations, it is not possible to find the form for the general 
vibrations in a corresponding manner, the single types of vibration only being 
independent of each other to a first approximation. 

We shall now determine the next approximations of the pure periodical type of 
vibration, of which the first approximation is defined by 



" -1 



= Ar" cos n3 sin qt, = - a" -1 A cos n$ cos qt, q" = ^(n 3 n). (14) 

q pa 



Second Approximation. 



From (6) and (7) we get 



and 



+ r 



a a 2 a' S3' a 3 '2a 3 a 

Introducing the values of (j>, {, q, defined by (14), in the terms of second order, 
we get 

^ + R>1 = _ n2 ( 2n ~ 1 ) a 2 -W cos 2nS sin 2qt+ ^ a 2 - 3 A 3 sin 2qt, (17) 
3t \_Sr_]r= a 4q 4q 

and 



4n 2) 
- 



8K-1) - 
Eliminating from (17) and (18), we get 



j / 1Q \ 

. . . (18) 



= _^ 3gn(n-l)(2n+l) a3n - 2 

4 ^71 T~ 1^ 



sin 2g. ( 1 9) 



SURFACE-TENSION OF WATER BY THE METHOD OF JET VIBRATION. 293 

Putting 

F (t) = qn (4n+ 3) a 2 "- 2 A a sin 2qt, 

(19) will be satisfied by 

4> = Ar" cos nS sin at *-, , ' \ n i A.V 2 " cos 2nS sin 2qt, (20) 

R i V'/) -t- 1 \ fiff 

when, as by first approximation, 

<7 2 / 3 ti^ /91\ 

w ~ i it it i, (^ A / 

pci 

Introducing this in (17), we get 

3 . A2 n 2 2n 3 -7n 2 -2n + 4 2n _ 3 

= na A cos n.9 sin ot+A - a cos 2%^ sin 2qt 

dt 4o 2w a +l 



- - (22) 
* 
from (22) we get 



=- Aa"- 1 cos n& cos at- A 2 - n \ 2n * 7n ' a 2 "- 3 cos 2A cos Iqt 

q 8r/ 2w J 



. (23) 
U 1 

Introducing in (18) the values found for </>, q, , and F' (i), we get 

= -A 2 ^ 



2 

which is satisfied by 

(24) 



By (8) we get in this case 

rj ^ A 2 ^2n-3 (25^ 

From (23), (24), and (25) we get 

-1 cos n& cos at A 2 ~ 3 a 2 "" 3 cos 2n9- cos 

8q* 2rt J +l 



+ A 2 / M ~ a 2 "" 3 cos 2n^-A 2 - 2 a 2 "" 3 cos 2 g ^-A 2 - a 2 "- 3 . . (26) 
S^ 2 2w 1 8q 3 8q* 



Third Approximation. 
From (6) and (7) we get 



._. 

8r 2 2 3r 3 r 3 95 8S r 2 Brfo 



294 MR. N. BOHR ON THE DETERMINATION OF THE 

and 



W 

Sr 2 8r 



2a 3 \3S/ a s 3 2 

- ..... < 28 > 

Introducing the values of <, , g, defined by (20), (21), and (26), we get (in order 
not to make the calculations more extensive than necessary, we will only calculate 
the terms which have references to the determination of q) 

fc - >coB ^ sin 

cos 2wS- sin 2gi + P 2 sin 2(/ + P 3 cos SnS- sin 3qt 
+ P 4 cos 3n5sin qt + ~P,,cosn9-sm 3qt ...... (29) 

and 



a a 

W 2 (w 2 -l)(40w s -24n 3 +65w-30) A3 3n _ 4 
= p i - t-i. i A'Vr cos n5 cos 



! cos 2n.^ cos 2qt + Q 2 cos 2w^ + Q 3 cos 2g^ + Q 4 
+ Q 5 cos 3n^ cos 3qt + Q 6 cos 3n5 cos qt + Q 7 cos ?i^ cos 3^. . (30) 



Eliminating from (29) and (30), we get 



3 3n _ 4 . 

= p i - L} V 4 cos n sin 

16(2n a +l)(2w-l) 



cos 2n sn 2(/i + 2 sn 2g^ + 3 cos 3n sn 
+ S 4 cos 3n& sin 5^ + 85 cos nQ sin 3^ ......... (31) 

Setting F (t) = S 2 sin 2qt, (31) will be satisfied by 

Q = Ar" cos n& sin g^ + Ajr 2 " cos 2n& sin 2^f + A 2 r 3 " cos 3n& sin 3gf 

+ A 3 r 3n cos 3w^ sin qt + A 4 r" cos n$ sin 3g, . (32) 
when 

e _ T . ,_ v A , 2n 
- n n 



SURFACE-TENSION OF WATER BY THE METHOD OF JET VIBRATION. 295 
Proceeding in the same manner as in the second approximation, we get 

{ = A a- [l -A' "I "' < n '-i> 9 ^'- 4 ^ a+8 T 5 r 6) l cos n< cos 3 , 
q L q 82(2n*-+l)(2n 1) J 

+ B! cos 2n cos 2qt + B 2 cos 2n3 + B 3 cos 2qt + B 4 

+ B 6 cos 3n& cos 3qt + ~B 9 cos 3n3 cos qt + E-, cos rt cos 3^, . (34) 



where the coefficients B!, B 2 , B 3 , B 4 are the same as in the second approximation, and 
the coefficients B 6 , B 6 , B 7 are of the same order as A 3 . 

As the result of the calculation we note [putting the coefficient of cos n5 cos qt in 
the equation (34) equal to 6], that the surface of a fluid-cylinder, executing pure 
periodical vibrations in two dimensions, can be expressed by 

7,2 r 0-3 _ n.-.V _ n n A 

r = a + bcos n& cos qt+ - \- , , cos 2n3 cos 2qt 

a I 8(2?i/+l) 



where 



In the experiments, the jets produced (stationary waves) will execute vibrations in 
three dimensions the cross-section will not be the same at different points of the jet. 
If, however, the velocity of the jet c is so great that the wave-length X is great in 
comparison with the diameter of the jet, the motion in the single cross-sections will 
differ very little from the motion in two dimensions, and the equation (35) can, 
therefore, also in this case give information about the form of the surface of the jet. 

The complete solution in three dimensions can be expressed by 

cos 2nS cos 2kz 



_. T,3 ,r y 
^ a a 



72f~ / \ 2 /\4 "H 

, - ! + !,! (^) +a 1 , 2 (~) +... 
a \_ \A./ \A./ J 



a 
and 



where the constant N 1; N 2 , ... arid M 1( M 2 , ... will be equal to the corresponding 

constants in the equations (35), putting in these equations t = - and q = 'In - = Tec. 

c c 

Neglecting the corrections in the terms of higher order in b/a, we get, using the 
formula of Lord EAYLEIGH for the wave-length of infinitely small vibrations in three 



296 MR. N. BOHR ON THE DETERMINATION OF THE 

dimensions [see (36), p. 288], and for sake of simplicity putting n = 2, which corresponds 
to the experiments executed, 

b" b 2 b a b a 

r = a+b cos 23- cos kz+ - cos 49 cos2&z-| -- cos 45 -- cos 2kz -- ... . (36) 

6a 4 8a 8a 

and 

(37) 



The equation (37) gives the correction on the wave-length sought. 
The equation (36) permits some further applications. 
Putting z = 0, we get 

r = a- +6 cos 2*+ -5- -cos 43.. (38) 

4a 12 a 

(38) is the equation for the form of the orifice (supposing that the velocity, at every 
point of the cross-section of the jet at the orifice, has the same magnitude and 
direction), when the jet is to execute pure periodical vibrations. We see from this 
that the opinion of P. O. PEDERSEN,* according to which a jet issuing from an orifice 
of the form (r = + /3cos25) must be expected to execute much purer vibrations 

/ 3 R 2 \ 

than a jet from an elliptical orifice r = a + yS cos 23+ - cos 45... ), is not correct. 

\ 4 a / 

Putting 5 = 0, we get 

r = H --- \-b cos kz-\ --- cos 2kz... (39) 

8a 24 a 

(39) is the equation for the wave-profile, formed by intersecting the surface of the 
jet by one of the two perpendicular planes of symmetry. Maximum- and minimum- 

values of r are obtained by putting in (39) respectively z = 2n-r and z = (2n-f 1) y. 

K K 

We thus get 

+ 7 Hi) alld i( 7 'mx.-nnin.) = & (40) 
DC*/ 

These formulas will be used in the measuring of the jets. 

Calculation of the Effect of the surrounding Air. 

We have hitherto neglected the density of the air.t A sufficient approximation of 
the small correction on the wave-length, due to the inertia of the air, is however very 
simply obtained by the following calculation regarding infinitely small vibrations in 
two dimensions of a cylindrical surface, separating two fluids of different density. 

* P. 0. PEDERSEN, loc. cit., p. 365. 

t Lord RAYLEIGH ('Phil. Mag.,' XXXIV., p. 177, 1892) has investigated the corresponding problem in 
the case where the symmetry about the axis of the fluid-cylinder is maintained during the vibrations. 



SURFACE-TENSION OF WATER BY THE METHOD OF JET VIBRATION. 297 

Considering the fluids as inviscid, we can suppose the existence of a velocity- 
potential <f). Putting 

we get 

9r 2 r 3r r 2 * 
which gives 

/(*) - 

As the velocity, as well inside as outside the cylinder-surface, must not be infinitely 
great, the potential inside the surface must be 



and outside 

< 2 = Br-V B 

Let the surface be expressed by 

r-a = = C 
For r = a the following conditions must be satisfied : 



From (1) we get 

B =^ Act 2 " and 

from (2) we get 



Introducing in (3) the values found for < 1; < 2 , and , we get 

T n a -n 



In the above we have investigated the influence on the phenomenon in question of 
the viscosity of the liquid, the magnitude of the wave-amplitudes, and the inertia of 
the air.* Collecting the results found, we get the following formula for determination 
of the surface-tension, setting n = 2, as will be the case in the experiments : 



..iat) I" /2t_r + 3 / ^ V] L + 37 V 
' (3 + 2 F) ia* J' a (tai) [ \pca 8 V Vca^/ J \ 24 a 2 ' 



* The corrections are to be considered as additive, since it can be shown that the wave-length also in 
the case of viscosity will be an even function of b/a. 
VOL. CCIX. A. 2 Q 



'298 MR. N. BOHR ON THE DETERMINATION OF THE 

Before proceeding to the experimental part of the investigation, we will yet 
consider a question which may be of interest for the discussion that follows. 

In the jets produced in the experiments the velocity must be supposed to be greater 
in the middle of the jet than closer to the surface. 

We can, however, in the following manner, get an idea of the rate at which the 
velocity-differences will be extinguished by the viscosity of the liquid. For this 
purpose we will consider a circular fluid-cylinder, in which each part moves with a 
velocity parallel to the axis of the cylinder, and in which the velocities of the different 
parts are only functions of the distance from the axis and the time. 

Using the axis of the cylinder as Z-axis, we have with the same notation as above, 

a = 0, fi = 0, and w=f(r,t). 
From the two first equations it follows that -^- = 0, arid, as further, p = const, for 



r 



r = a, we get p = const. 

Supposing w = (f> (r) e~ ft , the equation of motion 

Dw dp . 3 2 </> 1 3(4 pe , 

p,Vw-p -=- - = -f- gives _r + -- + L< = 0, 
Dt Sz or rtir p, 

of which the solution, subject to the condition to be imposed, when r = 0, is 

<f> = cJ (kr), in which P = - . 

P- 

The dynamical surface-condition gives ( ) = ; therefrom it follows that k must 



be a root of the equation 

J' v (ka) = 0, (k = 0, V* = irl'2197, k. 2 a = 7r2'2330, k 3 a = 7r3'2383,...). 
The general expression for iv is consequently 



_*."( 

w = Sr,,J &> e " . 



We see that the term of the expression for w containing J (k^r) decreases much 
more slowly than the terms with higher index. 

For the jets in question the term mentioned will furthermore be predominant 
already at the orifice, as dw/dr must be supposed to have the same sign between 
and a. 

The velocity in a jet-piece must therefore be expressed with a high degree of 
approximation by 

T n \ -. U/V1-2197Y 
w = c +f'iJ (AI?") e , where e = " I -1 , 

p \ a I 
t being the time which the jet-piece has taken to move from the orifice. 



SURFACE-TENSION OF WATER BY THE METHOD OF JET VIBRATION. 299 

Production of the Jet. 

The most important question in the experiments is to produce a jet which, while 
satisfying the suppositions made in the theoretical development, executes vibrations 
of a single type. 

This demand, however, cannot be expected to be satisfied by a portion of a jet of 
liquid which lies at a short distance from the orifice. Apart from possible variations 
of the value of the surface-tension on account of the very rapid extension of the 
surface, it will be very difficult to obtain pure harmonic vibrations of the jet at this 
place, for this requires not only a definite form of the cross-section of the jet at the 
orifice, but also a definite velocity at every point of this section. While it might be 
possible to satisfy the first condition by suitable choice of the orifice (see p. 296, (38)), 
it would, no doubt, be very difficult to satisfy the last ; among other reasons the 
velocity of the fluid will, for various causes, be greater in the middle of the jet than 
closer to the surface. It is, therefore, of great importance to produce a jet which is 
so stable that the vibrations can be examined at a considerable distance from the 
orifice where the viscosity of the liquid has had time to act. 

A jet issuing from a hole in a thin plate is, however, not very stable, and therefore 
the jet rather rapidly falls into drops. Tf, however, drawn-out glass-tubes are used 
as orifice, very long and stable jets can be formed when the tube has a suitable 
shape. 

In the experiments, jets were exclusively employed the qualities of which repeated 
themselves twice over the circumference. 

The orifices of the glass-tubes employed were given an elliptic section by specially 
heating the tubes, before drawing them out, on two opposite sides. Twisting of the 
glass-tubes would produce a rotation of the jet about its axis, and the planes of 
vibration would not preserve the same direction at different distances from the orifice ; 
to avoid such results it was necessary during the heating and drawing-out to have 
both ends of the tube fastened on slides which could be displaced along a 
metal-prism. 

When the glass-tubes were drawn out and cut off, they were examined under a 
microscope, and only those whose orifice had a uniform elliptic section were used. 
After this the jets, which were formed by the tubes, were examined. The purpose of 
this examination, which will be mentioned later (p. 307), was to find out if the jet was 
symmetrical about two perpendicular planes passing through its axis. 

It has been mentioned above that, because of the effect of viscosity, a portion of 
the jet will execute vibrations, which are in better conformity with those wanted the 
more removed it is from the orifice. It might here be of interest to illustrate this by 
an example. 

As such can be employed an experiment carried out with tube I (see the table on 
p. 310). 

2 Q 2 



300 MK. N. BOHE ON THE DETERMINATION OF THE 

The jet in question, which had a mean radius a = 0'0675 cm. and a velocity 
c = 425 cm./sec., was so stable that the wave-length could be measured with great 
exactness up to a distance of about 35 cm. from the orifice. We will now examine 
such a jet at a distance of 30 cm. from the orifice. 

The viscosity will firstly have the effect that an original difference in velocity at 
different points of the cross-section of the jet is rapidly extinguished. 

The calculation on p. 298 shows that the differences mentioned must decrease 
approximately as e~'\ where e = /A//O (7rl'2197/a) 2 . Let, now, a = 0'0675 and 
= Q'0125 (temperature 1 1 '8 C.), we get e = 40 '3. Let, further, t = -ffg, and we get 



e~ li = e~ 2 '"" = 0'0582. We see from this that the differences in velocity at the place 
in question must be about 17 times smaller than close by the orifice. 

The viscosity will furthermore have the effect that also the waves on the surface 
of the jet tend to be of single types. We found above that the general form of the 
surface of the jet, considering the vibrations as infinitely small, can be expressed by 



r = a + $& cos (n5 + T n ) cos (k n z + y M ) e 

where with approximation we have 

_ /u, 2n(nl) 



"" 1 



" p ca* 



Let now a = 0'OG75, p/p = 0'0125, c = 425 and z = 30, we get e~ v = 0'461, 
e -'* = 0-098, -*'-" = 0-0096, e~ v = 0'00043, e~ f " : = 0'000009, &c. 
If now the form of the surface of the jet is close to the orifice, 

r a + b 2 cos 23 cos k 2 z + b 3 cos 35 cos k 3 z + b t cos 4$ cos k 4 z + ... , 

the form of the surface will therefore be at a distance of 30 cm. from the orifice, 
approximately, 

r = a + (6 2 cos 25 cos k 2 z + }b 3 cos 35 cos A- 3 2 

+ -foh cos 45 cos l\z + TcroU^s cos 55 cos & 5 z +...). 



For the jet used, the term with cos 25 cos k a z was already at the orifice quite 
predominant, and especially the quantities b 3 , b 6 , ..., were very small in proportion to 
b 2 , as the jet at the examination mentioned was found to be very nearly symmetrical 
about two perpendicular planes through its axis. 

We thus see that the jet in the experiment mentioned at a distance of 30 cm. 
from the orifice rmist have executed exceedingly pure vibrations. 

In the experiments ordinary tap-water was used. 

For the sake of the investigation it was important to get a jet which could run 
without variation (same velocity and temperature) as long as wanted. In order to 
give the water a suitable constant temperature, it was led from the tap through a 
long leaden spiral tube, placed in a water-bath, and a regulator connected with the 



SURFACE-TENSION OF WATER BY THE METHOD OF JET VIBRATION 



301 



gasburner heating the bath. In this way the temperature of the water could be 
kept constant at 0'01 C. as long as wanted. 

The arrangement for keeping the pressure constant is shown in fig. 1. The water 
coming from the heating apparatus was led into a glass-bottle A, in which a constant 
water-level was maintained with help of an overflow B. From A the water was led 
down to the pressure-reservoir, consisting of two 5-litre glass-bottles C and D. 




Fig. 1. 

Inside C was placed an overflow E. G and D were connected by a wide bent-glass- 
tube F. H and K were two outlets through which the bottles could be emptied. 
From D the water was led down through a long glass-tube L to the jet-tube M. 
The whole arrangement was situated in a cellar, and the pressure-reservoirs as well 
as the jet-tube were supported by stone foundations. At the beginning of each 
experiment all the reservoirs and tubes were carefully cleaned and rinsed, whereupon 
the waterflow was adjusted so that a constant not particularly rapid flow ran through 
both the overflows. 

With the arrangement mentioned, the water- surface in the bottle D was very 
steady and quite independent of the variations of the pressure in the supply pipe. 

The temperature of the water was very near 12 C. in all experiments. 

In order to calculate the surface-tension of a liquid, the following quantities had to 
be known : (1) the density, p ; (2) the discharge per second. V; (3) the velocity of 



302 



MK. N. BOHE ON THE DETERMINATION OF THE 



the jet, c ; (4) the mean radius of the jet, a (which four quantities are connected by 
the relation V = pcira?); (5) the wave-length, and, finally for the correction, (6) the 
amplitudes of the waves. 

The density p of the tap-water used was at 1 2 found to be so near 1 (p = about 
I'OOOl) that by putting p = 1 only errors far below the exactness of the experiment 
were made. 

The measuring of the discharge presented no difficulty, and could be executed to 
0'02 per cent, of its value. 

Determination of the Velocity of the Jet.* 

When the jet is formed by a glass-tube, the velocity cannot be exactly calculated 
by the height of pressure on account of the friction in the tubes. In the present 





Fig. 2. 

investigation a direct method was therefore used to measure the velocity of the jet, 
the main features of which were as follows : In a fixed point the jet was cut 
through, at constant time-intervals, by help of a sharp and thin knife, and at the 



* A critical account of methods used in former investigations is to be found in the paper of 
P. O. PEDERSEN (loc. eit., p. 352). 



SURFACE-TENSION OF WATER BY THE METHOD OF JET VIBRATION. 303 

same time photographed instantaneously. Let the distance between two cuts, 
measured by help of the photographic plate, be a, and the time-interval be t, we have 
c = aft, c being the velocity of the jet. 

Fig. 2 shows the arrangement seen from above and from the side. 

The rotation -apparatus ABCD executes the cutting of the jet and the opening and 
closing of the light. A is a metal disk, to the edge of which the knives were fastened 
in radial direction. The knives, made from ground needles, measured about 0'4 mm. 
in width and were about 0'03 mm. thick. The axis of the rotation-apparatus was not 
parallel to the jet, but formed a small angle with it, so that the knife cutting through 
the jet had the same velocity parallel to the axis of the jet as the water-particles. 

D is a metal disk which has a radial slit close to the edge, which once at every 
revolution passes a corresponding slit in the screen E. The apparatus was driven by 
an electric motor, the speed of which could be regulated by means of an adjustable 
resistance, and, in order to make the velocity steady, the axis of the rotation- 
apparatus was provided with a small fly-wheel B. Further, to count the revolutions, 
the axis of the apparatus carried a contact C, which, completing the circuit of an 
electric current once at every revolution, marked a kymograph by help of an electro- 
magnet. The kymograph was also marked every second by another electromagnet. 

abcdefg provided for the illumination of the jet. By help of a powerful lens- 
system b an image of the horizontal linear filament of a Nernst lamp a was formed on 
the slit of the screen E. The mirrors c, e, f, and the lenses d and g, thereupon formed 
a magnified image of the slit on the jet, and from the lens g all the light was finally 
directed into the camera K. In the figure the dotted lines show the limitation of the 
beam of light. 

Every photograph was taken during about 12 seconds, which corresponded with 
about 600 revolutions of the apparatus with the following exposures of the plate- 
Some photographs are shown in the accompanying figure. (The direction of the jet is 




304 



ME. N. BOHR ON THE DETERMINATION OF THE 



from right to left.) We see how the ends of the jet set free by the knives very rapidly 
contract themselves into the corresponding jet-pieces, assuming a drop-like appearance. 

The plates were measured by examining them pressed together with a glass-rule 
under a microscope, and reading on the scale the positions of the lines, perpendicular 
to the jet, touching the drop-like free ends of the jet-pieces. Thereupon the mean of 
the results found for the two ends of each cut was calculated, and the difference 
between the means from two succeeding cuts, divided by the magnification of the plate, 
was equated to the distance which the jet had moved while the rotation -apparatus 
had made a revolution. The conditions of the correctness of this were partly that 
the cuts moved independently of each other, partly that the ends of the jet contracted 
themselves equally into the respective jet-pieces during the time which a cut took to 
move from the one place where it was photographed to the other. That these 
conditions were satisfied appears, first, from the fact that the part of the jet-pieces 
placed midway between the cuts was completely undisturbed by the cutting of the 
jet (see the photographs), and, secondly, from the symmetrical forms of the ends of 
the jet facing each other. 

The magnification of the plate was found by taking a photograph of a glass-rule 
placed directly under the jet. 

The interval of time between the cuts was determined as a mean from the number 
of revolutions per second during the time of exposure ; the photographic plate also 
giving a sort of mean of the single exposures, very great accuracy might be obtained 
in this way. 

At each determination of the velocity of the jet photographs were taken for the 
sake of the control with different times of revolution of the rotation-apparatus. 

The following table shows the result of an experiment by which four photographs 
were taken : 



Magnification of the 


Distance between 


Rotations per 


Velocity of the jet. 


photographs. 


two cuts. 


second. 


na 


f ' 


a. 


n. 


f 




cm. 




cm./sec. 


0-8624 


8-37 


40-19 


390-0 


0-8624 


6-735 


49-92 


389-8 


0-8624 


6-845 


49-15 


390-1 


0-8624 


6-54 


51-41 


389-9 



The values found show a very good agreement, the largest mutual deviation being 
less than O'l per cent. 

Determination of the Wave-Length. 

In the experiments, jets were used with so small wave-amplitudes that the wave- 
length could not be measured directly with sufficient accuracy either on the jet itself 
or on a photograph of the same. 



SURFACE-TENSION OF WATER BY THE METHOD OF JET VIBRATION. 305 

The method used to determine the wave-length consisted in finding out the 
summits of the jet (the points where the tangent-planes were parallel to the axis of 
the jet), using the jet as an optical image-forming system. 

Fig. 3 represents a horizontal jet-piece S (placed so that the two perpendicular 
planes of symmetry of the jet are respectively horizontal and vertical), a telescope T, 



M 



;B, 




L 



If 




Fig. 3. 



and a Nernst lamp L (the filament being vertical) fastened to the telescope 'in a 
position vertically over its axis, seen from above and from the side. OC^ is a 
horizontal line, perpendicular to the jet, through a summit. 

Seen from above, the jet acts as a lens with large focus- width, the front-surface of 
which will form a virtual image at A, and whose back-surface will form a real image, 
modified through the refraction during the double passage through the front-surface 
at B. Seen from the side, all the light reflected can, on account of the small diameter 

VOL. ccix. A. 2 B 



306 MR. N. BOHR ON THE DETERMINATION OF THE 

of the jet, be considered as intersecting the jet-axis. If, now, the telescope is focussed 
for the distance TA, a small vertical bright line a, and a less bright, but sharply 
limited ellipse /3, with horizontal great axis will therefore be seen in a dark field. 

When the telescope is displaced parallel to the jet, the distance between the bright 
line and the ellipse will vary, and the telescope being brought into a position quite 
opposite a summit, the bright line will fall together with the minor axis of the ellipse. 
Parallel to the jet was placed a fine glass-rule M, divided into -fa mm., which 
divisions could be seen sharply in the field of the telescope, together with the bright 
lines mentioned. 

The measurements were executed in such a manner that the telescope was partly 
displaced parallel to the jet and partly turned around a vertical axis, until the vertical 
spider-line fell together with the bright line at the same time as this halved the 
ellipse. 

Fig. 4 shows the appearance of the telescope-field. Every time when such an 
adjustment was obtained, the position of the spider-line was read on the glass-scale. 

The adjustment and reading could be done with an accuracy 
of O'Ol mm. 

In the above we have supposed that the jet-axis was 
horizontal. If, on the contrary, the jet formed an angle with 
the horizontal plane and this must be the case at certain 
places of the jet-piece examined on account of the curvature 
of the jet the bright line and the minor axis of the ellipse 
will form the same angle with the vertical spider-line. If, 
however, care was taken in the arrangement that the centre 
of the vertical line from the middle of the filament to the 
telescope-axis was at the same horizontal height as the jet, the vertical plane through 
the telescope-axis will here, too, as a closer examination shows, be perpendicular to 
the vertical plane containing the jet and go through a summit when the vertical 
spider-line goes through the middle of the bright line at the same time as this falls 
together with the minor axis of the ellipse. 

The circumstance that the wave-amplitudes on account of the viscosity of the 
liquid are decreasing in direction from the orifice has the effect that the distance OA 
between the focus-lines and the jet is not the same everywhere. While this fact is 
not of great importance when measuring the wave-lengths on a short jet-piece, it will, 
wheii measuring on very long jet-pieces (as in the table, p. 310) have the effect that 
the focussing of the telescope cannot be kept constant during the measuring, and the 
readings of the single summits could therefore, in this case, not be executed with 
quite as great accuracy as mentioned above. 

The differences between the readings indicate the distances between the projections 
of the summits on a horizontal plane. Dividing the mentioned differences by cos a, 
a being the slope of the jet at the place in question, we therefore get the distances 




SURFACE-TENSION OF WATER BY THE METHOD OF JET VIBRATION. 307 

between the summits. These distances can be directly put equal to the wave-lengths 
sought, for, considering the jet-axis as a straight line, the wave-profile can, apart 
from possible irregularities, be expressed with great approximation by (see p. 296) 

r = a + be~" cos kz-\ --- e~ 2e * cos 2kz-\ --- e~ 2 '~. 
24 a 8 a 

Finding the summits z n of this curve by putting 3r/3z = 0, we get approximately 



TT 



The first term on the right side is a constant, and with the values of e, k, and />/, 
which correspond to the experiments carried out, the second term is quite negligible 
as compared with the accuracy of the experiments. 

P. O. PEDERSEN has also measured the wave-length on a jet with very small wave- 
amplitudes. The author mentions* that it has not been possible for him to produce 
jets with such regular vibrations that he could use a method for the determination of 
the wave-lengths which he describes and which in the, main features is of the same 
nature as that described above. He therefore employed another method, which is, in 
the main, as follows : Illuminating the jet with a parallel beam of light, the rays 
twice refracted and once reflected form a wave-like image on a photographic plate, 
and as the amplitude of the image is much larger than that of the jet, the wave- 
length could be measured directly on the image. By this method the wave-length is 
determined as mean wave-length on a longer jet-piece. As however will appear 
from experiments, which will be described later, it is of the greatest importance to be 
able to determine the single wave-length with great enough accuracy for the 
variations of the wave-lengths to be examined. 

The image -format ion of the jet was also used in the examination of the jets 
mentioned on p. 299. If the tube was turned around its axis at the same time as the 
' images were observed in the telescope, the appearances of these changed as the 
curvature of the profile of the jet seen from above gradually varied, the points 
A and B being displaced. The variations in the appearance of the images were most 
rapid in the moments in which the curvature of the profile was near to O. Every 
time the curvature became O, the points A and B fell together and a regular elliptic 
luminous spot without structure was seen in the telescope. To the tube was fastened 
a disk with a graduation, and every time the luminous spot mentioned appeared in 
the telescope during the revolution of the tube the graduation was read oft'. If the 
jet were symmetrical with respect to two perpendicular planes, the places read off 
must lie symmetrical on the circumference of the circle and also be the same at 
different distances from the orifice. This examination was very sensitive and it 
showed, too, that not all of the tubes examined satisfied the conditions to a sufficient 

* PEDERSEN, foe. cit., p. 368, 
2 R 2 



308 ME. N. BOHR ON THE DETERMINATION OF THE 

degree of accuracy. However, four satisfactory tubes were found. That the jets 
produced by these four tubes executed exceedingly pure vibrations appears also 
very distinctly from the measurement of the wave-length, which will be mentioned 
later. 

In the experiments the jet had to be placed so that the two symmetrical planes were 
respectively horizontal and vertical. This was attained by turning the tube into a 
position midway between two of the above-mentioned readings. 

The Photographing of the Jet. 

To determine the magnitude of the amplitudes of the waves, magnified photographs 
of the jet were taken. 

Using nearly monochromatic light, and a special limitation of the illuminating 
beams, the profile of the jet was brought to appear with very great sharpness on the 
photographic plates. 

By help of an object-micrometer the diameter of the jet was measured at different 
places of the plate. The single diameters could in this way, on account of the 
sharpness of the outline, be measured with a relative exactness of about 0'03 per cent. 
of their value. 

From the largest and smallest diameter of the jet (2r max and 2r min ) the amplitude 

7, = f 1 "- 5 ^^ and the mean radius a = \ (r max . + ?- mill .) \l-\ (|)*1 [see p. 296 (40)] 

a 7 max. T / min. " L " \ a / J 

were determined. (On account of the decreasing of the amplitudes for r max . and r min 
respectively the mean of two succeeding r max and the r min lying between were used.) 

The value of the mean radius obtained in this way showed a very great conformity 
with the value which could be calculated by help of the discharge and the velocity 
of the jet, measured in the manner described above. 

In order to show this, two experiments (executed with the tubes I and IV) will 
be mentioned, by which the mean radius of the jet was determined in both ways : 

TUBE I. 

''max. 0-06929 cm., 0'06918 cm. Discharge V = 6'274 cm. 3 /sec. 

r mln . 0-06549 cm. Velocity c = 440'8 cm./sec. 



- = 0-0278, a = 0-06736 cm. a = A/ = 

<* V ifC 



0-06731 cm. 



TUBE IV. 

x. 0-08263 cm., 0'08255 cm. Discharge V = 7'862 cm. 3 /sec. 

to . 0-07777 cm. Velocity c = 390'0 cm./sec. 



- = 0-0301, a = 0-08017 cm. a = A/ = 

a V TTC 



O'OSOll cm. 



SURFACE-TENSION OF WATEE BY THE METHOD OF JET VIBRATION. 309 

We see that the mean radii a, determined in the two ways, are very nearly the 
same (mutual deviation less than O'l per cent.). This conformity having been stated, 
the velocity-determination was omitted at the later experiments and a was 
determined by help of the photographs only, whereby the experiments became very 
much simplified. 

The Results, of the Experiments. 

In the above we have described the methods used in the different measurements ; 
it is further mentioned how it was possible, by the arrangement described on p. 301, 
to keep the pressure-height and temperature of the water constant during the 
comparatively long space of time taken to determine the discharges, the velocity, the 
mean radius, and the wave-length. 

Before giving the results of the experiments we must, however, call attention to 
some special circumstances occurring in the determination of the wave-lengths sought, 
due to the fact that the wave-lengths found were not equal at different distances 
from the orifice. In order to show plainly what is meant by this, we shall commence 
with mentioning four experiments (one executed with each of the four tubes) carried 
out at a pressure-height of about 100 cm., in which the single wave-lengths were 
determined immediately outside the orifice and as far out on the, jet as its stability 
permitted. 

The results can be seen in the table overleaf. 

As it will be seen, the differences between the readings are not constant, but 
increase until they reach a maximum, whereupon they slowly decrease again. The 
same can be seen from the table on p. 311, where the numbers in the column 
designated by "mean values" are calculated from the table overleaf by a simple 
adjustment. 

The variation of the differences read off is, however, the result of many causes, 
among which are some the influence of which can be directly calculated. The first 
cause is the curvature of the jet, the effect of which is partly that the differences 
found are not equal to the real wave-lengths (see p. 306), partly that velocity and cross- 
section are not the same at different places of the jet-piece examined. The second 
cause is the decreasing of the wave-amplitudes, the influence of which appears from 
the equation (37) on p. 296. The column of the table on p. 311 designated by "corrected 
values " therefore contains wave-lengths, at different distances from the orifice, 
belonging to a horizontal jet which has the same velocity and cross-section as the jet 
examined on the horizontal place and which executes vibrations with infinitely small 
wave-amplitudes. 

We see that the numbers in the last-mentioned column increase until they reach a 
maximum, whereupon they keep very nearly constant. This seems to show that all 
the causes of the variation of the wave-length, the influence of which is not cor- 
rected for, must originate in irregularities ot the phenomenon which arise in the 



310 



MR. N. BOHR ON THE DETERMINATION OF THE 



Tube .... 


I. 


II. 


III. 


IV. 


Temperature . . . 


11-82C. 


11-73C. 


11-76 C. 


11-80C. 


Distance from the orifice ] 










of the ^ 


26 3 cm. 


29-4 cm. 


28-9 cm. 


34-6 cm. 


horizontal part of the jet J 










Discharge . . . 


6-100 cm. 8 /sec. 


7-678 cm. 3 /sec. 


7-720 cm. 3 /sec. 


8 649 cm. 3 /sec. 


Mean radius of the jet ~| 
on the horizontal place J 


0-06755 cm. 


0-07554 cm. 


0-07595 cm. 


0-08010 cm. 


Orifice . . . 


cm. 

o-o 


cm. 

o-o 


cm. 

o-o 


cm. 

o-o 


S' 


Summit I. 


0-99 


2-39 


2-375 


2-555 







2-03 


2-545 


2-525 


2-76 


10 
O 


II. . . 


3-02 


4-935 


4-90 


5-315 


o 




2-125 


2-56 


2-56 


2-765 





. III. . . 


5-145 


7-495 


7-46 


8-08 


o 




2-155 


2-575 


2-58 


2-795 


0} 


IV. . . 


7-30 


*10-07 


*10-04 


10-875 


a 




2-17 


2-605 


2-605 


2-83 


C3 


v. . . 


*9-47 


12-675 


12-645 


13-705 


X 
0) 




2-18 


2-635 


2-62 


2-85 


a 


VI. . . 


11-65 


15-31 


15-265 


*16-555 


^ 




2-195 


2-65 


2-63 


2-87 


| 


VII. . . 


13-845 


17-96 


17-895 


19-425 







2-215 


2-65 


2-64 


2-885 


o 


VIII. . . 


16-06 


20-61 


20-535 


22-31 


T3 - 




2-215 


2-655 


2-645 


2-895 


.2 


IX. . . 


18-275 


23-265 


23-18 


25-205 


a 




2-22 


2-66 


2-65 


2-90 





x. . . 


20-495 


25-925 


25-83 


28-105 


3 




2-22 


2-66 


2-655 


2-90 


15 


XI. . . 


22-715 


128-585 


128-485 


31-005 


-M 
a 




2-225 


2-655 


2-655 


2-90 



N 


XII. . . 


24-94 


31-24 


31-14 


133-905 


O 




2-225 


2-66 


2-655 


2-90 




XIII. . . 


t27-165 


33-90 


33-795 


36-805 


cS 




2-225 


2-655 


2-655 


2-90 


O 


XIV. . . 


29-39 


36-555 


36-45 


39-705 


03 

60 




2-22 


2-65 


2-65 


2 895 


.9 


XV. . . 


31-61 


39-205 


39-10 


42-60 


a 
BJ 




2-225 


2-65 


2-65 


2-895 


& [ XVI. . . 


33-835 


41-855 


41-75 


45-495 


b C* 
The amplitude on 


0-0417 


0-0699 


0-0640 


0-0382 


the summits | 










designated by * and t Lf 


0-0258 


0-0472 


0-0432 


0-0276 



SURFACE-TENSION OF WATER BY THE METHOD OF JET VIBRATION. 311 



formation of the jet and which are rapidly extinguished. We see, however, that the 
influence of these irregularities on the wave-length is not insignificant, even at a 
considerable distance from the orifice. Thus, in the experiments mentioned, the 
wave-lengths are at a distance of 10 cm. from the orifice in the mean 2 per cent., and 





I. 


II. 


III. 


IV. 


Distance from 










the orifice 


















in centimetres. 


Mean 


Corrected 


Mean 


Corrected 


Mean 


Corrected 


Mean 


Corrected 




values. 


values. 


values. 


values. 


values. 


values. 


values. 


values. 


5 


2-14 


2-148 


2-55 


2-553 


2-54 


2-545 


2-76 


2-782 


10 


2-185 


2-189 


2-59 


2-591 


2-595 


2-597 


2-815 


2-829 


15 


2-210 


2-211 


2-640 


2-638 


2 625 


2-624 


2-850 


9-859 


20 


2-221 


2'221 


2-654 


2-650 


2-642 


2-639 


2-880 


2-884 


25 


2-225 


2-224 


2-658 


2-653 


2-652 


2-648 


2-896 


2-897 


30 


2-224 


2-224 


2-658 


2 654 


2 656 


2 652 


2-900 


2-899 


35 








2-656 


2 653 


2-654 


2-652 


2-901 


2 899 


40 








2-651 


2-652 


2-650 


2 -052 


2-898 


2-898 



at a distance of 20 cm., 0"3 per cent., smaller than is the wave-length at a distance of 
30 cm. from the orifice ; if, therefore, the wave-length at 10 cm. or at 20 cm. distance 
from the orifice had been used for the calculation of the surface-tension, a value 
respectively 4 per cent, and O'G per cent, too great would have been obtained. 

The four experiments mentioned furthermore illustrate the influence of the viscosity 
on the phenomenon, the magnitude of the wave-amplitudes at two places of the jet 
with considerable mutual distance being measured (see the table on p. 310). 



Putting - = A.e ", we get for the four jets respectively 

(Jb 



e = 0-0271, e= 0-0212, 

In the above we have found (p. 289 (40)) 



e = 0-0213, 



e = 0-0187. 



p ca" \ rz, /L ( 2\pcd 2 k/ 
From this formula we get the following results for /*, 

in = 0-0131, p. = 0-0129, p. = 0-0130, ^ = 0-0129. 

We see that these values do not differ much from the most generally adopted value 
for p., namely, /x = 0-0125 (temperature, ITS C.). That they, however, are all greater 
suggests, perhaps, a very small superficial viscosity. 

The correction of the formula to calculate the surface-tension, due to the effect of 
the viscosity on the wave-length, is, according to the equation (41), on p. 289, deter- 
mined by the coefficient 



\pca" 



312 



MR. N. BOHR ON THE DETERMINATION OF THE 



By introducing the values for //,, p, c, a, and k, which correspond to the experiments 
carried out, this correction becomes very small, about O'l per cent.* 

As to the calculated correction for the influence of the finite wave-amplitudes, it 
may be mentioned that the values of the surface-tension in the table of the experiments 
on p. 313, which has been calculated according to the formula (37) on p. 296, does 
not show any systematic deviation due to the wave-amplitude. 

As, however, the correction for the value of the wave-amplitude in the experiments 
carried out is rather small (from O'lO per cent, to 0'33 per cent.), the agreement 
mentioned is not adapted to give an experimental verification of the formula 
theoretically developed. It may here be remarked that P. O. PEDERSEN (loc. cit., 
p. 371) has experimentally investigated the influence of the value of the wave- 
amplitudes upon the calculated values of the surface-tension and has found results, by 
using greater wave-amplitudes, which can be shown to be in very good agreement 
with the formula in question. 

In the other experiments the wave-length was measured only on a shorter jet-piece, 
which, however, was so far from the orifice that the value of the wave-lengths had 
become constant. 

As an example of such a measurement, an experiment with tube I may be mentioned, 
which was carried out with a pressure-height of about 70 cm. 

In the table below are quoted two sets of readings, obtained in succession, with 
their differences. 



Readings. 


Difference. 


Readings. 


Difference. 


cm. 


cm. 


cm. 


cm. 


1-819 




1-818 






1-796 




1-797 


3-615 




3-615 






1-798 




1-800 


5-413 




5-415 




1-799 




1-800 


7-212 




7-215 






1-801 




1-799 


9-013 




9-014 






1-799 




1-799 


10-812 




10-813 






1-796 




1-797 


12-608 




12-610 





The horizontal place of the jet was at a distance of 21 '5 cm. from the orifice, which 
corresponded to a reading on the glass-rule of 7 '5 cm. Corrections of the readings 

* The smallness of the correction is due to the email coefficient of viscosity (/* = 0-0125) and the great 
surface-tension (T = 74) of water. The correction mentioned can, however, become quite considerable for 
liquids in which these quantities have other values ; if, for example, aniline (p = 062, T = 44) was 
used, the correction would have been more than 1 per cent, by corresponding experiments. 



SURFACE-TENSION OF WATER BY THE METHOD OF JET VIBRATION. 



313 



have not been introduced, as they were in this case very small ; thus the correction 
for the decreasing of the wave -amplitudes would become completely imperceptible on 
account of the small value of the amplitudes. Besides, the very small decrease of the 
utmost differences corresponds to the one to be expected on account of the curvature 
of the jet. 

We see that the wave-lengths are very constant, and that the jet at the place in 
question must have executed exceedingly pure vibrations, because only a small 
deviation from pure harmonic vibrations must involve considerable irregularities of 
the differences between the readings. 

The other experiments carried out show results very similar to those described 
here. It may be remarked that, a priori, we could expect exceedingly pure 
vibrations of the jets from all the four tubes. The circumstance that the regular 
variation of the differences between the readings commenced directly past the orifice 
(see the table on p. 310) shows that already at this point we had to do with what was 
very nearly a single vibration only, and, as mentioned on p. 300, the vibrations of the 
jet must be much purer at a considerable distance from the orifice than close to it. 

The table below contains the result of all the experiments carried out. The surface- 
tension is calculated according to the following equation (see p. 297) : 



2 



Tube. 


Temperature. 


Discharge. 


Mean radius. 


Wave-length. 


Amplitude. 


IV 




C. 


cm. 3 /sec. 


cm. 


cm. 




dyne/cm. 


I. 


11-8 


6-100 


0-06755 


2-225 


0-026 


73-24 


I. 


11-4 


5-608 


0-06758 


2-039 





73-41 


I. 


11-3 


4-965 


0-06767 


1-800 





73-34 


II. 


11-7 


7-678 


0-07554 


2-658 


0-046 


73-01 


II. 


11-2 


7-076 


0-07567 


2-443 





72-98 


II. 


11-4 


6-272 


0-07587 


2-154 





73-26 


III. 


11-8 


7-720 


0-07595 


2-656 


0-042 


73-45 


III. 


11-4 


6-290 


0-07604 


2-157 





73-28 


IV. 


11-8 


8-649 


0-08010 


2-901 


0-027 


73-21 


IV. 


11-9 


7-984 


0-08014 


2-677 





73-09 


Mean value of the experiments with Tube I 


73-33 





73-08 


T) 


73-37 


)) )) !> )I A* 


73-15 


Mean value of all experiments . . 


73-23 



We see that the mutual agreement between the single determinations is very good 
(the greatest deviation from the mean value being about 0'35 per cent.). 

It may be remarked that in the values found for T 12 no indication of a distinct 
VOL. ccix. A. 2 s 



314 MR. N. BOHR ON THE DETERMINATION OF THE 

influence originating either from the variation of the diameter of the jet, or of the 
discharge, or of the amplitudes of the waves can be found. 

In all the experiments mentioned, tap-water was used. An investigation was, 
however, carried out to see if a different result would be obtained by using distilled 
water instead of tap-water. For this purpose two large reservoirs were filled respectively 
with distilled and tap-water. After the contents of the reservoirs had assumed the 
same temperature, measurements of wave-lengths in exactly the same conditions were 
undertaken on a jet of each of the two sorts of water by connecting first the one 
reservoir and then the other with the glass-bottle A, fig. 1, by a siphon. The 
experiment, which was repeated several times, showed that no sensible difference was 
to be found between the two jets. 

This result was also to be expected from previous investigations on the surface- 
tension of water. 

Now proceeding to compare the value found here with values found by previous 
determinations, we shall not try to give a complete account of the very extensive 
literature on this subject. The table opposite contains only the results of a few of the 
investigations of later years, which are generally considered the most important for 
the estimate of the value of the surface-tension. 

The table shows rather considerable deviations between the values found by the 
different investigators. As an explanation of these deviations, the question of the 
purity of the surface has been among the most prominent, relying on the fact that the 
tension of a water-surface may decrease very considerably when the surface becomes 
contaminated with even an extremely small amount of foreign substances. This 
circumstance, however, does not seem sufficient to explain the deviations among the 
values found by authors who have used the same method for purifying the surface 
(e.g., GRUNMACH and KALAHNE ; FORCK and ZLOBICKI). 

The fact that a number of authors (e.g., VOLKMANN, DORSEY, FORCK) who have 
worked with different methods have found such exceedingly good conformity among 
the results of their single experiments after all seems to show that the surface-tension 
of a carefully purified surface is a very constant quantity. This assumption is further 
confirmed by the circumstance that several authors (KALAHNE, DORSET, &c.) have 
not found any sensible diminishing of the surface-tension during the time of the 
experiment. 

The results of the investigations by Miss A. POCKELS,* Lord B,AYLEiGH,t and 
F. NANSEN| on the influence of contaminations upon the tension of a water-surface 
seem also highly to point in this direction. 

In consequence of the above-mentioned, it therefore seems that a great deal of the 

* A. POCKELS, 'Nature,' XLIIL, p. 437; XL VI., p. 418; XLVIIL, p. 152. 'Ann. d. Phys,' VIII., 
p. 854. 

t RAYLEIGH, ' Phil. Mag.' XLVIIL, p. 321, 1899. 

t F. NANSEN, 'Norweg. North Polar Exped. Sclent. Results,' 10, 1900. 



SUEFACE-TENSION OF WATER BY THE METHOD OF JET VIBRATION. 



315 



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316 ME. N. BOHR ON THE DETERMINATION OF THE 

deviations in question must be explained not by real differences of the surface- 
tension, but by the methods used in measuring this tension. 

We now proceed to consider more closely some of the investigations mentioned, 
and compare the results with that found in the present paper. 

We will commence with P. 0. PEDERSEN'S investigations, as his determination of 
the surface-tension of water is executed by the same method (jet- vibration) as 
that used by the author. PEDERSEN finds, as the table shows, a value which is 
considerably greater (about 2 per cent.) than the value here found. As, however, 
PEDERSEN has not examined the variations of the wave-length, but only determined 
the wave-length as mean wave-length on a jet-piece at a comparatively short distance 
from the orifice, the cause of the difference between the value found by PEDERSEN 
and the author- may be that PEDERSEN probably has used too small a value for the 
wave-length (see p. 311). 

Among the other methods to determine the surface-tension, the capillary-tube 
method and the method of capillary ripples are those mostly used and generally 
considered the most important. 

Among the investigations carried out by the former methods, VOLKMANN'S must 
be especially mentioned on account of the excellent agreement between the single 
experiments whicli he has obtained, taking great care in the measurement of the 
dimensions of the tubes and in their purification. This agreement, being independent 
of the dimensions of the tubes and of the nature of the glass, seems to have taken 
away the foundations of the criticism of the results which the capillary-tube method 
can give. VOLKMANN finds, as is seen, a value which lies rather near the author's, 
the difference being, however, about 0'7 per cent. 

As is to be seen from the table, a great number of investigations have recently 
been executed by the method of capillary ripples. We see that the values found by 
this method are generally higher than the value found in this paper. The mutual 
conformity between the results of the different investigations is however not very 
great. In the author's opinion this disagreement depends on the fact that in many 
cases the conditions of the experimental investigations do not sufficiently correspond 
to the assumptions on which the theoretical development rests ; in what follows, an 
attempt has been made to show what is meant by this. 

The experiments executed by the method mentioned can be divided into two 
groups, according to advancing rectilinear waves, produced by help of the vibrations 
of a glass plate fastened to one prong of a tuning-fork, or standing waves formed by 
interference between two systems of advancing circular waves, generated by two pins 
fastened to both prongs of a tuning-fork, being used. 

Among the 'authors who have used the former method, only DORSEY and 
KoLOWRAT-TscHERWiNSKi seem to have examined the magnitude of the wave-length 
at different distances from the generator. Both of the investigators found 



SUKF ACE-TENSION OF WATEK BY THE METHOD OF JET VIBRATION. 317 

considerable irregularities near the generator, the wave-length here being dependent 
on the distance from the plate and first becoming constant at a greater distance from 
this. The authors mentioned, being aware of this fact, used for calculating the 
surface-tension only the length of waves which were at a certain distance from 
the glass-plate (DORSEY 4 cm., and KOLOWRAT-TSCHERWINSKI 8 cm.). As the 
wave-length near to the glass-plate was larger than further out, this may explain the 
fact that DORSEY and especially KOLOWRAT-TSCHERWINSKI have found lower values 
than other investigators who have used the same method, but as it seems have not 
taken precautions in this direction. 

The other method, using the standing waves, suffers, as also KOLOWRAT- 
TSCHERWINSKI remarks, from certain defects, because the measuring of the wave- 
length taking place on the straight line which connects the above-mentioned pins, 
those waves only can be examined which are at so short a distance from the pins that 
there is no security of the phenomenon being sufficiently regular. On account of 
this the results found by this* method do not seem to be very reliable, especially the 
very high values of the surface-tension, and the great deviations between the result 
of the single experiments found by GRUNMACH, BRUMMER, and LOEWENFELD may 
probably be explained by the very small distance (1'8 cm.) between the pins used by 
these investigators. KALAHNE, who employs the same method, but has a distance of 
7 cm. between the pins, also finds a value considerably lower and with a much better 
mutual conformity than the above-named investigators. 

In consequence of these considerations it does not seem necessary for the author to 
conclude that the method of capillary ripples in reality gives a value essentially higher 
than the one found by the method described in this paper. 

Conclusions. 

In the present determination of the surface-tension of water the method of jet- 
vibration proposed by Lord RAYLEIGH is used ; this method has the fundamental 
advantage that a perfectly fresh new-formed surface can be examined. 

In the first part of this investigation it is shown how Lord RAYLEIGH'S theory of 
infinitely small vibrations of a jet of non-viscid liquid can be supplemented by 
corrections for the influence of the finite amplitudes as well as for the viscosity. 

In the experimental part of this investigation an attempt has been made to show 
how in a simple manner it seems to be possible to secure that the jet-piece used for 
the measurement satisfies the assumptions on which the theoretical development 
rests. 

As the final result of his experiments the author finds the surface-tension of water 
at 12 C. to be 7 3 '23 dyne/cm. 



[ 319 ] 



XIII. On the Osmotic Pressures of Calcium Ferrocyanide Solutions. 

Part II. Weak Solutions. 

By the EARL OF BERKELEY, F.R.S., E. G. J. HARTLEY, B.A. (Oxon.), 
and J. STEPHENSON, B.Sc. (Land.). 

Received January 16, Read February 18, 1909. 

IN the following communication the experiments on the direct measurements of the 
osmotic pressure and the densities have been carried out in conjunction with 
Mr. HARTLEY, while those on the electric conductivities were with Mr. STEPHENSON. 

The reason for choosing calcium ferrocyanide as solute were given in Part I., but it 
may be added that weak solutions of this salt showed certain interesting anomalies, 
to be described later, which made it desirable to measure their electric conductivities 
with a view to throwing some light on the connection between osmotic pressure and 
ionisation. 

The process followed in purifying the salt has already been given in Part I.,"" and 
eo has that used in obtaining the densities. 

The Measurements of Osmotic Equilibrium Pressures. 

These measurements are confined to solutions whose equilibrium pressures are under 
25 atmospheres. The apparatus was the same as that previously described in the 
account of our experiments on sugar solutions (' Phil. Trans.,' Series A, vol. 206, p. 482), 
except that the large dead-weight pressure-gauge was replaced by a smaller one 
specially made by Messrs. Schiiffer and Budenberg, which seemingly allowed accurate 
measurements to be obtained down to 2 '5 atmospheres pressure, and at the same time 
the increment of pressure (loc. cit., p. 498) was O'l atmosphere. t 

It had been thought that by increasing the area of the membrane (but keeping the 
genei'al construction of the apparatus the same) these lower pressures would be 
measurable to a greater degree of accuracy that is to say, that for a small change 
in pressure a larger quantity of water would pass through the membrane and 
consequently give a bigger effect on the reading of the water-gauge. Some 50 
porcelain tubes, supposed to be similar to those used previoiisly in paste porosity 
and diameter (but 20 cm. in length), were therefore obtained from the makers. 
Unfortunately all efforts to obtain even one membrane good enough for accurate work 
failed, and the attempt has had to be abandoned for the time being ; consequently the 
experiments were done with the short tubes. 

* ' Phil. Trans.,' Series A, vol. 209, p. 179. 

t This apparatus was compared with the mercury column at the National Physical Laboratory and 
found correct. 

VOL. CCIX. A 453. 26.5.09 



320 THE EARL OF BERKELEY, MESSRS. E. G. J. HARTLEY AND J. STEPHENSON 





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ON THE OSMOTIC PRESSURES OF CALCIUM FERROCYANIDE SOLUTIONS. 321 



Results of Density and Equilibrium Pressure Measurements. 

The foregoing table gives the results obtained : Column (l) gives the date ; (2) the 
weight concentration, i.e. the number of grammes of anhydrous salt to 100 gr. of water ; 
(3) the density of the solution at C. ; (4) the percentage content of water in the 
hydrated salt ; (5) the tube employed ; (6) the apparent turning-point, that is, the 
point at which there was no observable movement of the water-level in the gauge ; 
(7) the guard-ring leak (see Part I.) ; (8) the time the pressure was on the solution ; 
(9) the quantity of anhydrous salt passed through the membrane ; (10) the change 
in the water-level caused by the increment of pressure ; (11) the apparent turning- 
point corrected for guard-ring leak ; in this case it is the equilibrium pressure. 

The following table gives the mean values derived from Table L, together with the 
theoretical osmotic pressures calculated on the assumption that BOYLE'S law holds for 
these solutions. 

Column (1) gives the weight concentration, i.e. the number of grammes of solute to 
100 gr. of solvent ; (2) gives the corresponding densities ; (3) the number of gram- 
molecules of anhydrous salt in the litre of solution ; (4) the corresponding equilibrium 
pressures ; (5) the osmotic pressure calculated from BOYLE'S law, assuming 
KT = 22-41. 

All molecular weights have been calculated with H = 1. 

TABLE II. 



(1.) 


(2.) 


(3.) 


(4.) 


(5.) 


Weight 
concentration. 


Density at C. 


Number of 
gram-molecules of 
anhydrous salt in 
litre of solution. 


Observed 
equilibrium 

pressure. 


Osmotic pressure 
(BOYLE'S law). 








atmospheres 


atmospheres 


21-813 


1-16287 


0-7175 


20-33 


16-08 


17-610 


1-13444 


0-5853 


14-65 


13-11 


12-213 


1-09592 


0-4110 


9-20 


9-21 


7-072 


1-05716 


0-2406 


5-34 


5-39 



The agreement at the two lower concentrations between the BOYLE'S law osmotic 
pressures and those directly observed is remarkable. But as calcium ferrocyanide 
solutions are conductors of electricity, and therefore presumably ionised to a 
considerable extent, we should expect the observed osmotic equilibrium pressures to 
be higher than the calculated. This discrepancy led to similar work being done on 
solutions of strontium and potassium ferrocyanides, and the following tables give the 
results. 

VOL. CCIX. A. 2 T 



322 THE EARL OF BERKELEY, MESSRS. E. G. J. HARTLEY AND J. STEPHENSON 



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ON THE OSMOTIC PRESSURES OF CALCIUM PERROCYANIDE SOLUTIONS 323 



The meaning and numbering of the columns are the same as in Table I., with 
the exception that for the potassium salt column (4) is omitted because the salt, 
which was purchased as Messrs. Kahlbaum's purest, was not systematically analysed* 
for its water content. 

In the following table the mean values are given, and the columns are numbered 
and have the same significance as in Table II. 

TABLE IV. 



(1.) 


(2.) 


(3.) 




Weight 
concentration. 


Density. 


Number of 
gram-molecules 
per litre. 


( 

cc 

] 








a 


13-580 


1-08575 


0-3547 




8-897 


1-05810 


0-2362 




5-631 


1-03775 


0-1512 


3-035 


1-02085 


0-08216 


1-518 


1-01050 


0-04129 



Observed 

equilibrium 

pressure. 



atmospheres 

19-25 
13-52 
9-19 
5-41 
2-93 



(5.) 



Osmotic 

pressure 

(Bovi.K's law). 



atmospheres 

7-95 
5-29 
3-39 
1-84 
0-93 



It will be noticed that these results are such as would be expected on the 
dissociation hypothesis ; the greater the dilution the greater the ionisation, until at 
the greatest dilution there is apparently dissociation into about three ions or 
molecules. 

A few experiments were made with strontium ferrocyanide to see whether the 
same anomalies (see p. 321) obtained as those shown by the calcium salt. The salt 
was purchased from Messrs. Kahlbaum and purified by recrystallisation as in the case 
of the calcium salt. 

Analyses gave the following results : 





1st lot 
from 
Kahlbaum. 


2nd lot 
from 
Kahlbaum. 


1st lot 
recrystal- 
lised. 


2nd lot recrystallised. 


Percentage composition 
calculated from salt 
containing 


15 Aq. 


14 Aq. 


Sr 


per cent. 

27-28 
32-87 
38-86 


per cent. 

27-15 
38-89 


per cent. 

27-47 
33-02 
39-31 


per cent. 
39-40 


per cent. 

27-97 
33-69 
37-80t 


per cent. 

26-64 
32-28 
41-08 


per cent. 

27-39 
33-19 
39-42 


Fe(CN) (i . . . 
H.,0 . . . . 


99-02 




99-80 




99-46 


100-00 


100-00 



* An analysis of the salt gave 12-81 per cent. H 2 O. Theoretical 12-78 per cent. 
t The sample was taken from a lot which was known to have been overdried. 

2 T 2 



324 THE EARL OF BERKELEY, MESSRS. E. G. J. HARTLEY AND J. STEPHENSON 

It will be apparent that the salt when dried in an air current, at about 20 C., 
contains 14 of water, and not 15 as stated by ROSCOE and SCHORLEMMER.* 

The following table gives the results of the osmotic-pressure determinations, and 
the figures in the columns have the same meaning as in the case of Table I. 

TABLE V. Strontium Ferrocyanide. 



(1.) 


(2.) 


(3.) 


(4.) 


(5.) 


(6.) 


(7.) 


(8.) 


(9.) 


(10.) 


(11.) 


Date. 


Weight 
concen- 
tration. 


Density 
at C. 


Per- 
centage 
of Aq 
in salt. 


Tube. 


Apparent 
turning 
point. 


Guard- 
ring 
leak. 


Time. 


Solution 
leak. 


Rate 
of 
move- 
ment. 


Equi- 
librium 
pressure. 












atmospheres 




hours 




nun. 


atmospheres 


Nov. 23, 1908 23-99 1-19253 


37-83 


N 


12-07 -0-3 


3 


Nil 


1-3 


12-04 


Dec. 4, 1908. 17-97 1-1-1690 38-60 N 


8-58 +0-1 


2| 


Nil 


1-0 


8-59 


July 21 ,1908 13-51 1 11314 ! 39-31 N 6'40 


-0-2 


3 


0-0004 0-9 


6-38 


Nov. 10, 1908 1 12-51 ; 1-10470 37 -87 N 5-98 







Nil 


1-7 


5-98 


Nov. 26, 1908 6-199 ; 1-05302 37'79 j X 


3-38 


+ 0-2 


3 


Nil 


1-6 


3-39 


Dec. 29, 1908 6-161 1-05281 38-90 


N 


3-40 





3 




1-5 


3-40 



Tabulating these results in the form given for the calcium and potassium salts, 

TABLE VI. Strontium Ferrocyanide. 



we get : 



(1.) 


(2.) 


(3.) 


(4.) 


(5.) 


Weight 
concentration. 
Number of grammes 
of salt in 100 Aq. 


Density at C. 


Gram-molecules 
in the 
litre of solution. 


Observed 
equilibrium 
pressure. 


Osmotic pressure 
(BOYLE'S law). 








atmospheres 


atmospheres 


23-99 


1-19253 


6000 


12-04 


13-45 


17-97 


1-14690 


0-4542 


8-59 


10-18 


13-01 


1-10892 


0-3320 


6-18 


7-44 


6-180 


1-05291 


0-1594 


3-40 


3-57 



In the case of this salt the observed osmotic equilibrium pressures are less than 
those calculated from BOYLE'S law ; thus the peculiarity noticed in the case of the 
calcium salt is emphasised in the strontium solutions. 

A search for a similar anomaly was made among such other salts of complex acids 



1 Treatise on Chemistry,' vol. ii., p. 1025 (1897 edition). 



ON THE OSMOTIC PEESSURES OF CALCIUM FERROCYANIDE SOLUTIONS. 325 



as would be likely to give satisfactory osmotic pressures, but without results, as will 
be seen by the following list : * 





Observed 


Osmotic 




Substance. 


equilibrium 
pressure 


pressure 
(BOYLE'S 


Remarks. 




at C. 


law). 






atmospheres 


atmospheres 




Magnesium camphorate. . . 


7-85 


7-61t 


Preliminary experiment. 


,, . . . 


5-91 


4-36 


Accurate osmotic pressure of recrystallised salt. 


99 ' * 


6-09 


4-33 


,, ,, 


Potash alum 


2-13 


0-682 


Accurate osmotic pressure. 


Sodium naphthionate . . . 


9-4 


6-32 


Preliminary experiment. 


1! ... 


10-07 


6-34 


Accurate osmotic pressure of rccrystallised salt. 


Barium benzene sulphonate . 


13-0 


5-75 


Preliminary experiment. 


,, 


13-86 


5-72 


Accurate osmotic pressure of recrystallised salt. 


Lead benzene sulphonate . 


12-48 


5-16 


Preliminary experiment. 


Potassium benzene sulphonate 


15-81 


8-69 


,, 


Barium o-nitrobenzoate. . . 


16-85 


6-63 




j> ... 


16-01 


6-20 


Accurate osmotic pressure of recrystallised salt. 


Calcium naphthionate . 


3-75 


1-85 


Preliminary experiment. 


,, ,, ... 


3-95 


1-79 


Accurate osmotic pressure of recrystallised salt. 


Luteo cobalt chloride . . . 


6-67 


2-94 


Preliminary experiment. 


Calcium acetate 


5-20 


2-36 


Accurate osmotic pressure not recrystallised. 




29-4G 


13-26 













t This experiment was done with an imperfect membrane. 

The Electric Conductivities of the Solutions. 

The cell used for the stronger solutions is shown in fig. 1 ; it was originally designed 
for another research (the conductivities of saturated solutions), but was found quite 
satisfactory for the present purpose. A is the cell proper, and B and C its electrodes ; 
these are covered with platinum black in the usual manner. The solution, which is 
contained in the beaker D (capacity about 250 c.c.), is sucked up into the cell by 
means of the tap E, and the resistance is determined by the Fitzpatrick and Whetham 
commutating method.^ 

As the osmotic pressures were determined at C., it was imperative, for the 
purpose of comparison, to obtain the conductivities at the same temperature. This 
was secured in the following way : The whole apparatus was plunged into ice and 
the stirrer started ; when the temperature was constant at or near C., the solution 
was sucked up into the cell and its resistance determined ; the cell was then emptied ; 
after an interval of three or four minutes it was refilled and the resistance 
re-determined. These operations were repeated until a constant resistance was 
obtained. The temperature was always noted before and after every operation, and 
observations in which there had been a change of more than 0'01 C. were rejected; 

* We are now experimenting with the ferricyanides for the same purpose. 
I ' Phil. Trans.,' A, vol. 194, p. 330. 



326 THE EARL OF BERKELEY, MESSRS. E. G. J. HARTLEY AND J. STEPHENSON 

such a change very seldom happened when the proper level of the liquid in the beaker 
had been found. The first observation, however, of any series was nearly always 
somewhat different from the subsequent ones ; this was thought to be caused by a 
slight difference of concentration on the electrode surfaces when first wetted by the 
solution, and the observation was therefore rejected. 



-Thermometer 




Solution | =*_ . 



Fig. 1. 



Temperature Coefficient. 

As the temperature of the solution was always some seven or eight hundredths of 
a degree above 0C., a correction was obtained by allowing the temperature to rise 
slightly and then re-determining the resistance ; by assuming that the change of 
resistance was proportional to the change of temperature the observed resistance 
could be extrapolated to C. 

It may be mentioned here that although the level of the solution in the cell could 
not be seen on account of the mercury jacket (see fig. 1), yet by means of an oil gauge 
attached to E it was ensured that on filling the cell the level always reached the 
same height. 



ON THE OSMOTIC PRESSURES OF CALCIUM FERROCYANIDE SOLUTIONS. 327 



Resistance Box. 

The coils of the box were of manganin, and were tested by means of a calibrated 
platinum bridge wire having a standard-ohm coil joined to each end. Coils of the 
same nominal value were thus compared and the results calculated in terms of the 
coil of highest resistance (5000 ohms), thus* giving the value of a box ohm. In no 
case was the deviation greater than aifooth of the nominal value. 



Resistance Capacity of the Cell. 

The cell was standardised by means of an approximately normal solution of 
potassium chloride. The specific conductivity of this solution is given by Kolil- 
rausch (see LANDOLT and BOKNSTEIN'S tables) for temperatures from 0. upwards. 
The salt used was Merck's purest, and care was taken that it was thoroughly dry 
before weighing out the necessary quantity. 

Three separate sets of observations were made and the results are tabulated 
below : 



Concentration. Grammes 
of KC1 in 
100 gr. solution. 


Resistance in ohms 
at C. 


Specific conductivity 
of the 
solutions at C. 


Resistance capacity 
of cell. 






cm~ ' ohm" 1 


oil ni s 


7-1322 


13 GO -2 


0-06535 


88 89 


7-1357 


1359-2 


0-06538 


88-87 


7-1386 


1359-4 


0-06541 


88-92 



A normal solution of potassium chloride contains 7'1385 gr. of salt in 100 gr. of 
solution and has a specific conductivity of 0'06541 at C. ; the specific conductivities 
given in the table are calculated from this by assuming that the conductivity is 
proportional to the concentration. 

It is worth noting that on* increasing the speed of revolution of the commutator so 
that the alternations of current were changed from 36 to 72 per second no appreciable 
change in the resistance of the solution was engendered. 

Resistance of the Solutions. 

As there was but little salt at our disposal the solutions were made up in the 
following way : The salt for the strongest solution required was weighed out (a 
suitable portion from the same bottle being set aside for the analysis of its water 
content) and the weight of water added determined on the balance. A part of this 
solution was used for the resistance experiments, and the other part, after weighing, 
was diluted and again weighed, and so on ; thus the weight concentration of each 
solution used for the conductivity work was known, and the density corresponding to 



328 THE EARL OF BERKELEY, MESSRS. E. G. J. HARTLEY AND J. STEPHENSON 

the concentration could be obtained from the graph of these two quantities which had 
already been determined in the osmotic-pressure experiments. 

The water used for the dilution was distilled, in a Jena glass still, from a dilute 
solution of potassium di-chromate, and its resistance determined in another cell to be 
described later. 

The table on p. 329 is a copy of the Record of a typical experiment with calcium 
ferrocyanide. 

The columns 1, 2, and 3, under the heading temperature, require a word of 
explanation. The temperature under 1 is that of the solution just before the cell was 
filled, 2 gives it just after the measurement of the resistance, and 3 just after 
emptying. 

The solution contained '93023 gr. of anhydrous calcium ferrocyanide in 100 gr. of 
solution. 

The ratio arms were 10 : 100 and the battery gave 2 volts. 

Resistance of the Solutions at Infinite Dilution. 

Although, as is well known, the relation between the conductivity at infinite 
dilution and that at finite concentrations is not well established for salts of the 
molecular complexity of the ferrocyanides, yet it was thought that this relation might 
throw some light on the discrepancy indicated on p. 321. Experiments on very dilute 
solutions were therefore undertaken. 

Low -resistance Cell. 

A cell for this purpose was kindly lent by Mr. WHETHAM ; it was made of Jena 
glass and is shown in fig. 2. The electrodes D and E are coated with platinum 
"grey" to prevent the absorption of salt, which, as pointed out by WHETHAM,* 
generally takes place when platinum black is used. The cell was suspended in a 
beaker of ice and water, and this in its turn was placed in ice. 

Make up of the Solutions. 

The water used was twice distilled in the ordinary way and then redistilled from 
potassium di-chromate, the middle third only being used. All glass vessels and 
pipettes were of Jena glass and the water and solutions were stored in stoppered Jena 
glass flasks. 

Resistance Capacity of the Cell. 

The cell was standardised by means of a solution of potassium chloride containing 
0'007352 gr. of salt in 100 gr. solution. This solution was obtained as follows: A 

* Loc. cit. 



ON THE OSMOTIC PEESSURES OF CALCIUM FERROCYANIDE SOLUTIONS. 329 





Temperature of the 




Deflection 










solution. 




of galvanometer. 












Galvano- 




Box 


Resist- 




Time. 








meter 






resist- 


ance of 


Remarks. 










zero. 


Left 


Right 


ance. 


solution. 






1. 


2. 


3. 




key 


key 


















down. 


down. 








P.M. 


C. 


C. 


C. 








ohms 


ohms 




1.0 


























Made up solution. 


5.20 


0-285 









0-2R 


0-2L 


3332 











0-280 







0-1R 


0-05L 


3333 





> Rejected. 








0-285 





0-1L 


0-1R 


3334 33334 


J 


5.26 


0-285 









0-1L 


0-1R 


3334 










0-285 


0-285 








3333 


33330 




5.31 


0-290 


285 










0-05R 3333 












0-285 





0-1R 


0-1L 3332 


33328 




5.36 


0-290 


0-285 







0-1R 


0-1L ; 3332 










0-290 











3333 


33330 




5.41 


0-290 


0-285 













3333 












0-290 





0-1R 


0-1L 


3332 


33330 




Mean = 


0-289 












Mean = 


33330 




6.32 


0-320 


0-310 


0-320 







0-1L 



0-1R 


3332 
3333 33320 


> Rejected. 


6.37 


0-325 


0-315 













3330 










0-325 





0-1R 


0-1L 3329 


33300 




6.42 0-325 


0-320 







0-1R 


0-1L 3329 










0-330 











3330 


33300 




6.47 ; 0-330 


0-325 







0-2L 


0-2R 


3331 















0-1L 0-1R 3330 












0-330 





0-05R 


0-05L 3329 


33293 




Mean = 


0-327 












Mean = 


33298 





The emergent column correction was - 0-038 
thermometer zero -0-175 



Total -0-213 

For the 1st set of observations the true mean temperature was 0-076 C. ; mean resistance, 33330 ohms. 

2nd 0"-114,, 33298 

For a change of temperature of 038 C. the change of resistance was 32 ohms. 

Therefore taking the mean of all the observations, and correcting for temperature, the resistance of the 
solution at C. was 33393 ohms. 

solution of N/25 was first made up accurately by weight ; 10 gr. of this was added to 
400 gr. of conductivity water in flask A. At the same time as the water was added 
to flask A, a similar quantity of the same water was poured into flask B. Both flasks 
were kept stoppered, and whenever one flask was opened for any purpose the other 
was opened for the same length of time and in the same place. In this way it was 

VOL. CCIX. A. 2 U 



330 THE EARL OF BERKELEY, MESSRS. E. G. J. HARTLEY AND J. STEPHENSON 

hoped that any contamination from the atmosphere would affect both equally, and by 
determining the resistances of the water and solution in the following order water, 
solution, water, solution, water and taking the mean values, we should thus get a 
close approximation to the conductivity of the salt in the cell. 



Bobber 
plug- 




Stirrer 



Mercury 



Fig. 2. 

Using Kohlransch's* value for the conductivity of N/1000 potassium chloride 
(reduced to C. by means of D^OUISNE'S temperature coefficientf) and correcting it 
for the slight difference in concentration between N/1000 and our solution, we get the 
resistance capacity of the cell = 0'4539 ohms. 

Resistance of the very Dilute Solutions. 

A stock solution of each salt was made up and this was used as in the case of the 
standard potassium solution ; it was found, however, that all of the very dilute 

* LANDOLT and BORNSTEIN'S tables, 1905, p. 756. 
t LANDOLT and BORNSTEIN'S tables, 1905, p. 755. 



ON THE OSMOTIC PRESSURES OF CALCIUM FERROCYANIDE SOLUTIONS. 331 

solutions decreased slightly in resistance with lapse of time, except the most dilute of 
all, which increased with the time.* In each case a time coefficient was determined 
by experiment, and the resistances given in the tahles are the resistances the solutions 
would have had immediately after being made up. 

It was also noticed that, with the low-resistance cell, the rate of alternation of 
current had a perceptible effect on the resistance ; a great number of experiments 
were made to determine the cause of this, but without result. It was, therefore, 
decided to make all measurements at a speed which, on the whole, gave the most 
consistent results. 



Results for Calcium Ferrocyanide. 

The results for the calcium ferrocyanide are collected in the following table. The first 
seven lines refer to solutions whose constants were determined in the high-resistance 
cell and the remainder refer to the low-resistance cell. 



TABLE VII. 



Weight of 
salt in 100 gr. 
of water. 


Number of 
gramme 
equivalents in 
the litre. 


Specific 
conductivity 
of the solution 
at 0' C. 


Specific 
conductivity 
of the water 
at C. 


Specific 
conductivity 
of the salt 
in the solution 
at 0" C. 


Equivalent 
conductivity 
of the salt 
at 0' C. 






cm." 1 ohm" 1 


cm." 1 ohm" 1 


cm." 1 ohm" 1 




17-779 


2-3632 


0-03545 





0-03545 


0-01500 


7-1265 


0-9696 


0-01782 





0-01782 


0-01838 


3-6294 


0-4972 


0-0,9492 





0-0,9492 


0-01909 


1-8570 


0-2552 


0-0,4998 


0-0 5 20 


0-0,4996 


0-01957 


0-9390 


0-1292 


0-0,2661 


0-OjU 


0-0,2660 


0-02059 


0-4385 


0-06040 


0-0,1369 


0-0.,15 


0-0,1368 


0-02265 


0-2109 


0-02906 


0-0 3 7470 


0-0,10 


0-0 3 7460 


0-02567 


0-021794 


0-0 2 3004 


0-0,1259 


0-0 S 0965 


0-0 3 1249 


0-04158 


0-010875 


0-0,1499 


0-0 4 7349 


0-0,0959 


0-0 4 7253 


0-04839 


0-007245 


0-0 3 9986 


0-0 4 5357 


0-0,0937 


0-0 4 5263 


0-05270 


0-004345 


0-0 3 5989 


0-0 4 3584 


0-0 5 1005 


0-0 4 3484 


0-05817 


0-002413 


0-0 3 3326 


0-0 4 2225 


0-0,0981 


0-0 4 2127 


0-06395 


0-001204 


0-0 3 1660 


0-0 4 1254 


0-0 6 1068 


0-0 4 1147 


0-06910 



The equivalent conductivities of the stronger solutions are plotted against the 
concentrations in diagram 1, and those of the very dilute solutions are plotted against 
the cube root of the concentrations in diagram 2 ; the latter curve when extrapolated, 
as shown by the dotted lines, to infinite dilution gives the probable limits between 

* The greatest decrease observed was 03 per cent, per hour, while the increase in the most dilute 
solution of the calcium salt was 0- 10 per cent, per hour, and for the strontium salt 0-14 per cent. 

2 U 2 



332 THE EARL OF BERKELEY, MESSRS. E. G. J. HARTLEY AND J. STEPHENSON 

which the value of the equivalent conductivity at that dilution (= p.J) lies ; that is, 
between 0'074 and 0'09. 



Results for Strontium Ferrocyanide. 

These results are given in Table VIII. The first five lines refer to the stronger 
solutions ; they practically cover the range over which the osmotic pressures were 
measured, and thus, in conjunction with the equivalent conductivity at infinite 
dilution, afford an insight into the relative dissociation of the salt. The last six lines 
refer to the very dilute solutions. 

TABLE VIII. 



Weight of 
salt in 100 gr. 
of water. 


Number of 
gramme 
equivalents in 

the litre. 


Specific 
conductivity 
of the solution 
at C. 


Specific 
conductivity 
of the water 
at C. 


Specific 
conductivity 
of the salt 
in the solution 
at C. 


Equivalent 

conductivity 
of the salt 
at 0" C. 






cm." 1 ohm" 1 


cm." 1 ohm" 1 


cm."" 1 ohm" 1 




24-010 


2-4019 


0-03487 





0-03487 


0-01452 


13-398 


1 3662 


0-02316 





0-02316 


0-01695 


10-288 


1-0548 


0-01847 





0-01847 


0-01751 


7 3265 


7545 


0-01356 





0-01356 


0-01797 


3-7169 


3849 


0-0,7116 





0-0,7116 


0-01849 


03040 


0-0,3162 


0-0 3 1291 


0-0 S 1018 


0-0 3 1281 


0-04051 


0-01517. 


0-0,1577 


0-0 4 7730 


0-0-,1055 


0-0 4 7624 


0-04834 


0-01010 


0- 0,1051 


0-0.j5549 


0-0;,0981 


0-0 4 5451 


0-05187 


0-0,6058 


0-0 3 6301 


0-0 4 3724 


0-0,1039 


0-0 4 3620 


0-05745 


O-Q.,3364 


0-0 3 3499 


0-0 4 2336 


0-0,1057 


0-0 4 2230 


0-06373 


0-0,1678 


0-0 3 1746 


0-0 4 1337 


0-0 6 1086 


0-0 4 1228 


0-07035 



The numbers are plotted in diagrams 1 and 2 in the same way as in the case of the 
calcium salt. 

From the curve of the very dilute solutions the value at infinite dilution will be 
seen to lie between 0'076 and 0'098. 



Theoretical Considerations. 

From the foregoing conductivity results it will be seen that both the calcium and the 
strontium solutions are fair conductors of electricity, yet if we judge from the osmotic- 
pressure experiments alone, the calcium salt should show no appreciable dissociation, 
while the strontium salt shows that there must even be some association. 

A tentative explanation of these facts may be based on either of two hypotheses : 



ON THE OSMOTIC PRESSURES OF CALCIUM FERROCYANIDE SOLUTIONS. 333 



(1) that the salts in solution are associated* into double molecules, and these are 
ionised, or (2) that the salts are ionised single molecules, and the ions are themselves 
aggregated into larger complexes. 



026 



O24 



Ordinates are Che equivalent conductivities. 

Abscissae are the gram equivalents per litre of solution. 

Curve (I) refers to the calcium solutions . 



(2) 



strontium 



(I) 



018 



O16 





1-0 



1-5 



2-0 



2'5 



3-0 



Diagram 1. 



The first hypothesis is the more simple (it admits of a suitable chemical formula 
being postulated), and if by its aid we can explain the facts, it will not be necessary 
to consider the second. 

Assuming, then, that the molecules are double, we shall get the following tables, in 

* Cp. RAOULT (" Tonometrie," ' Scientia Series,' No. 8, p. 90) on the association of the sulphates of 
divalent metals as evidenced by the lowering of the vapour pressures of the solutions. 



334 THE EARL OF BERKELEY, MESSRS. E. G. J. HARTLEY AND J. STEPHENSON 

which column (l) gives the weight concentration ; (2) the number of douhle gram- 
molecules in the litre of solution (=N); (3) the equivalent conductivity of the 
solution (=/"); (4) the ratio fj./fjt- x , where /A M is the equivalent conductivity at infinite 



09 



08 



07 



06 



05 



04 



\ \ 

\ \ Abscissas are the cube root of the number of grains, of 

\ \ anhydrous salt in too gra. solution. 

\ \ Curve (i) refers to the calcium solutions. 



Ordinates are the equivalent conductivities.' 



\\ 



(2) 



strontium 



\Y 

\ \ 

\ \ 

-^ \ \ 



;v 

X \ 



\ 





Diagram 2. 

dilution, and is assumed to be the mean of the limits given by the curves on diagram 
(2) ; (5) gives the osmotic pressure (= P) calculated from the well-known equation 



ON THE OSMOTIC PRESSURES OF CALCIUM FERROCYANIDE SOLUTIONS. 335 

where n (= 6) is the number of ions into which the molecule is split up ; column (6) 
gives the observed osmotic equilibrium pressure. 

TABLE IX. 



(1-) 


(2.) 


(3.) 


(4.) 


(5.) 


(6.) 


Weight 
concentration. 
Number of 
grammes of 
anhydrous salt 
to 100 gr. Aq. 


Number of 
double 
gram-molecules 
in litre of 
solution. 
N. 


Equivalent 
conductivity of 
the salt in 
solution. 
P- 


Jf_ 
ft." 


Osmotic 
pressure 
calculated for 
6 ions. 
P. 


Observed 
osmotic 
equilibrium 
pressure. 
EP. 










atmospheres 


atmospheres 


Calcium Ferrocyanide. 


17-610 


0-2926 0-01506 0-184 12-59 14-65 


12-213 


0-2055 0-01700 0-207 9-37 9-20 


7-072 


0-1203 0-01840 0-224 5-71 


5-34 


Strontium Ferrocyanide. 


23-99 


0-3000 0-01452 0-167 12-33 12-04 


17-97 


0-2271 


0-01603 0-184 


9-77 


8-59 


13-01 


0-1660 


0-01702 0-196 


7-37 


6-18 


6-180 


0-0797 


0-01816 


0-209 


3-65 


3-40 



If we take into consideration the various assumptions involved in calculating the 
numbers in column (5). the agreement between these and the observed osmotic 
pressures is as good as could be expected, but it should be mentioned that as good an 
agreement can be obtained if the double molecule be assumed to be split up into 
5 ions.* 

A simple chemical formula which will express these results is 



Ca(CN) ; 
Ca(CN)/ 



/(CN) 3 Ca 
Fe = Fe/ V 



\(CN) 8 Ca ' 



where the ions are the four Ca and two Fe(CN) 6 , while a corresponding formula applies 
to the strontium salt. This formula was originally proposed by ERLENMEYERf for 
the ferrocyanides, and it is of interest to see whether, in the case of the potassium 
salt, a similar molecule, ionised into the corresponding number of ions, namely 10, 
will bring the calculated and observed osmotic pressures into agreement. 

Using JONES and WEST'S^ measurements of the conductivities of potassium 

* In this case the constitutional formula gives four Ca ions and one {Fe(CN),;};>. 
t 'Lehrbuch Org. Chem.,' 1867, p. 148. 
t ' Amer. Chem. Jour.,' 34, 1809, p. 392. 



336 



THE OSMOTIC PEESSUEES OF CALCIUM FEEEOCYANIDE SOLUTIONS. 



ferrocyanide solutions at C. and treating the results in the same way as that 
adopted for the other salts, but keeping to their own units, we get for the double 
molecule and 10 ions the following table, where /u,^ = 8 8 '5. 

TABLE X.- Potassium Ferrocyanide. 



(1.) 


(2.) 


(3.) 


(4.) 


(5.) 


(6.) 


Weight 
concentration. 
Number of 
grammes of 
anhydrous salt 
to 100 gr. Aq. 


Number of 
double 
gram-molecules 
in litre of 
solution. 
N. 


Equivalent 
conductivity of 
the salt in 
solution. 
^- 




fi^ 


Osmotic 
pressure 
calculated for 
10 ions. 
P. 


Observed 
osmotic 
equilibrium 
pressure. 
EP. 










atmospheres 


atmospheres 


13-580 


0-17735 


40-1 


0-453 


20-18 


19-25 


8-897 


0-1181 


40-6 


0-459 


13-57 


13-52 


5-631 


0-0756 41-7 


0-471 


8-88 


9-19 


3-035 


0-04108 


43-9 


0-496 


5-03 


5-41 


1-518 


0-02064 


47-7 


0-539 


2-72 


2-93 



The agreement between the numbers in columns (5) and (6) seems good enough to 
warrant the conclusion that the assumption of double* molecules ionised into 10 ions 
is not incompatible with the facts. On the other hand, it may be pointed out that 
the deviation from the theoretical BOYLE'S law osmotic pressure may be considerable, 
for it is apparent in cane-sugar solutions even down to some 7 atmospheres pressure ; 
in view of the uncertainty of the value of the conductivities at infinite dilution, 
together .with the weakness of the theory which connects them with the conduc- 
tivities of _ the solutions themselves, it was considered useless to attempt to correct for 
these deviations. 

Reviewing the evidence recorded in this communication, it may be concluded that 
the calcium and strontium salts are proved to be associated when in solution, and it is 
possible that they exist as the double molecules of the formula given on p. 335. 

* Cp. BUCHBOCK'S work on aqueous solutions of tetraethyl ferrocyanide (' Zeit. Phys. Chem.,' 23, 1897, 
p. 157), shows the molecule to be (C 2 H 5 ) 2 Fe(CN)o. In view of the known tendency for organic iso- 
cyanides to be formed from certain metallic cyanides, it may be that this substance is constituted 
differently to the metallic ferrocyanides. 



f 337 ] 



XIV. On the Spontaneous Crystallisation of Monochlor acetic Acid and its 

Mixtures wit/t Naphthalene. 

By Principal HENRY A. MIEKS, F.R.ti., and Miss FLORENCE ISAAC, Research 
Felloiv of Somerville College, Oxford. 



Received January 26, Read February 18, 1909. 



CONTENTS. 

Page 

Introduction preliminary experiments on mixtures of naphthalene and monochloracetic acid . 338 

PART I. MONOCHLORACETIC ACID AND ITS AQUEOUS SOLUTIONS. 

A. The different modifications of monochloracetic acid 340 

a-modification 311 

/3-modification 341 

/-modification 342 

B. Transformations of the modifications of monochloracetic acid . . . '. 342 

Transformations of 7 342 

Transformation of /3 343 

C. Aqueous solutions of monochloracetic acid 343 

Method of experimenting by observation of refractive indices 343 

Solutions giving an a-shower 345 

Solutions giving a /3-shower 345 

Solutions giving a y-shower 349 

I. Tabulated results of solutions of various concentrations first giving a-showers leading to 

the a-supersolubility curve 350 

II. Tabulated results of solutions first giving /3-showers leading to the /J-supersolubility 

curve 353 

III. Tabulated results of solutions first giving y-showers leading to the y-supersolubility 

curve 356 

IV. Monochloracetic acid stirred in an open vessel 359 

V. Verification of the supersolubility curves by experiments with sealed tubes 360 

1. Tubes giving a-showers 362 

2. Tubes giving /3-showers < 362 

3. Tubes giving y-showers 363 

4. Outlying points 363 

VOL. CCIX, A 454. 2 X 27.5.09 



338 PRINCIPAL HENRY A. MIERS AND MISS FLORENCE ISAAC ON' THE 

Page 

VI. The solubility curves for the different modifications of monochloracetic acid 364 

1. The a-solubility curve 366 

2. The /3-solubility curve 366 

3. The y-solubility curve 367 

VII. Relative positions of the a-, /?-, and y-solubility and supersolubility curves 367 

VIII. Additional experiments with pure monochloracetic acid 368 

PART II. MIXTURES OF NAPHTHALENE AND MONOCHLORACETIC ACID. 

Introduction 369 

I. The solubility curves 370 

1. Solubility of naphthalene in monochloracetic acid 371 

2. Solubility of the a-modification of monochloracetic acid in naphthalene .... 371 

3. Solubility of the /^-modification of monochloracetic acid in naphthalene . . . . 371 

4. Solubility of the y-modification of monochloracetic acid in naphthalene . . . . 372 

II. The supersolubility curves 372 

1. The naphthalene branch of the supersolubility curve 375 

2. The a-branch of the supersolubility curve 375 

3. The /J-branch of the supersolubility curve 375 

4. The y-branch of the supersolubility curve 376 

Discussion of results and conclusion 376 

Introduction. 

OUR previous papers on spontaneous crystallisation have dealt with the supersolubility 
curves, firstly, of pure substances ; secondly, of mixtures of two or more substances 
which do not form mixed crystals ; and, finally, with naphthalene and /8-naphthol ; 
the last form mixed crystals of the type (l) of ROOZEBOOM, in which the freezing- 
points of all mixtures lie between the freezing-points of the pure components. 

The object for which the present investigation was undertaken was to study the 
spontaneous crystallisation of two substances which form mixed crystals and possess a 
minimum or eutectic freezing-point. 

Monochloracetic acid and naphthalene, as described by CADY (' Journ. Phys. 
Chem.,' 1899, 3, p. 127), seemed to supply convenient material for this purpose. For 
monochloracetic acid melts at 62 C. and naphthalene at 79 0- 9, both these temperatures 
lying within a range suitable for the methods which we had previously employed. 
According to CADY, the mixture containing 2 9 '4 per cent, naphthalene and 70'6 per 
cent, monochloracetic acid has a minimum melting-point of 53'5, and is, therefore, 
the eutectic mixture. CADY also conducted a series of experiments which enabled 
him to trace both the melting-point and the freezing-point curves in both sides of the 
eutectic, and he found them to be separated by a considerable interval. These curves, 
therefore, appear to have been well established, and we thought it would be ohly 
necessary for us to trace the supersolubility curves and find their relation to the 
curves determined by CADY. We began by attempting to verify his freezing-point 



SPONTANEOUS CRYSTALLISATION OF MONOCHLORACETIC ACID, ETC. 339 

curve and melting-point curve. Preliminary experiments tended to confirm the 
former, but we were unable to verify the latter. Further, the microscopic examin- 
ation of the mixtures containing excess of naphthalene above the eutectic compo- 
sition showed that all the crystals which separated in the early stages of consolidation 
possessed the form and the optical properties of pure naphthalene. This led us to 
doubt whether any mixed crystals whatever are formed in these solutions, and to 
suspect that monochloracetic acid and naphthalene yield in reality only another 
example of the crystallisation of the two pure substances from their mixtures, like 
the mixtures of salol and betol which we have already investigated. On the one 
side of the curve, representing excess of naphthalene above the eutectic composition, 
we were able to trace a perfectly definite supersolubility curve separated by about 
2'5 from the solubility curve ; this supersolubility curve belongs to crystals possessing 
the form and optical properties of naphthalene. On the side of the curve corre- 
sponding to mixtures containing excess of monochloracetic acid above the eutectic 
composition, we again obtained evidence of a definite supersolubility curve, separated 
in this instance by about 10 from the solubility curve, but for these mixtures 
spontaneous crystallisation appeared also to take place at several other very well 
defined temperatures. Experiments made upon drops of these mixtures viewed under 
the microscope, with the object of determining the optical properties of the mixed 
crystals which we then expected to find, proved very difficult to interpret, and led us 
to suspect that crystals of two or three distinct sorts were making their appearance in 
addition to crystals of naphthalene. We also obtained no less than three different 
temperatures of spontaneous crystallisation for pure monochloracetic acid. 

In a paper on the properties of acetic acid, and its chloro- and bromo- derivatives, 
published in the ' Journ. Chem. Soc.,' 1895, 67, p. 664, PICKERING traced the freezing- 
point curves of three distinct modifications of monochloracetic acid, which he 
distinguished as a, ft, and 8, together with indications of a fourth modification which 
he called y. It therefore seemed probable to us that the multiple freezing-points of 
the mixtures containing excess of monochloracetic acid may really belong to the 
different modifications of this substance, and that none of these mixtures really yield 
homogenous mixed crystals of monochloracetic acid and naphthalene. If so, the study 
of these two substances would not yield any information concerning the spontaneous 
crystallisation of mixed crystals possessing a minimum freezing-point, but they might 
provide material for an even more interesting study that of the spontaneous crystal- 
lisation of the different modifications of a substance dissolved in another substance 
which is not polymorphous. We were led thus to begin with an investigation of 
monochloracetic acid and its solution in water with the object of ascertaining the 
solubility and supersolubility curves of the different modifications from aqueous 
solutions. There is at present no evidence which proves that each modification of a 
polymorphous substance possesses a definite and different temperature of spontaneous 
crystallisation. 

2x2 



340 



PRINCIPAL HENEY A. MIERS AND MISS FLORENCE ISAAC ON THE 



PART I. MONOCHLORACETIC ACID AND ITS AQUEOUS SOLUTIONS. 
A. The Different Modifications of Monochloracetic Acid. 

The first accurate measurements of the crystals obtained from solution in water 
were given by SCHMELCHER (' Zeits. f. Krystallographie,' 1892, vol. 20, p. 115), who 
described them as belonging to the monoclinic system with the elements 

a : 6 : c = 0-8176 : 1 : 0-5G33 ; /3 = 70 43', 
and as presenting the forms 

B = {010}, p = {2W}, o = {lll}, = {Oil}. 

The angles are : 

pp = 42 12', 

qq =56 5', 
oo = 42 0', 
oij = 26 30', 
op = 39 40'. , 

The plane of cleavage, B, is perpendicular to the third mean line ; and there is also 
a good cleavage parallel to (100). (See fig. 1.) 





B 



FIG. I. 



FIG. 2. 



As was pointed out by PICKERING (' Journ. Chem. Soc.,' 1895, vol. 67, p. 664), there 
are in reality certainly three, if not four, modifications to be distinguished. 

The crystals described by SCHMELCHER were obtained from solution in water. 

The following are the appearances presented by the substance as it cools from fusion 
or crystallises from aqueous solution. 



SPONTANEOUS CRYSTALLISATION OF MONOCHLORACETIC ACID, ETC. 341 

a-modification. The crystals most frequently obtained on a microscope slide, 
whether from aqueous solution, from solution in alcohol, or from fusion by slow 
cooling, are plates which appear to be identical with the crystals described by 
SCHMELCHER. They have the form shown in fig. 2, with plane angles : 

PO = 137 (43), 
OQ = 152 (28), 
QP = 71 (109). 

From SOHMELCHER'S measurements the corresponding angles would be 

100 : 101 = 42 48', 

101 : 001 = 27 55', 
001 : TOO = 109 17', 

and capital letters are assigned to the edges on fig. 2 corresponding to those of the 
taces on fig. 1. 

The microscopic crystals are elongated plates extended along the edge P (= pp), 
and generally terminated by the edge O (= 06) ; sometimes also by the edge Q (= qq). 
The extinction is nearly parallel to the edge O, and 
therefore makes an angle of 43 with the length of 
the crystals (the edge P). The double refraction, 
which is strong, is compensated by a quartz wedge 
inserted with its axis perpendicular to the edge O. 

The crystals melt at about 61, and are therefore 
the modification called a by PICKERING. 

They sometimes present the form of rhombs having 
a plane angle of 71, when they are bounded by the 
edges PQ alone ; they can then be identified by the 
extinction angles 43 and 28 respectively, measured 
with regard to the two edges of the rhomb. 

^-modification. These crystals can be obtained 
best from solution in water ; the cooling solution 
sometimes yields the a-modification and sometimes 
the ft. They can be obtained direct in a drop of F I G . 3 . 

solution by scratching the slide under the cooling 

drop ; but the most convenient way of obtaining ft is to produce y by rapid cooling 
and to transform it into ft by friction. They seem to be difficult to obtain directly 
from fusion. 

They generally present the form shown in fig. 3 stout tables of rhombic outline 
belonging to the monoclinic system. 

B = 010, C = 001, m = 110. 




342 PRINCIPAL HENRY A. MIERS AND MISS FLORENCE ISAAC ON THE 

The measured angles are 

mm = 52 20', 

Cm = 73 40'. 

From these measurements the angle /8 = 100 : OOl, or the plane angle of the face B, 
is calculated as 71 44-g-'; the plane angle on the face C is 54 43', and that on the 
face m is 81 43'. There is a good cleavage parallel to B; the extinction on C is 
straight, and that on B makes an angle of about 23|- with the edge C, and about 
48|- with the edge m, while on m it makes an angle of about 36 with the edge mB. 
The face B is perpendicular to the third mean line. The crystals possess strong 
positive birefringence, and not a very large axial angle. The acute positive bisectrix 
is inclined at 23|- to the edge BC and at 48| to the edge Bm. The refractive index 
appears to be greater than that of the a-moclification. 

On a microscope slide crystals which appear to be identical with these are sometimes 
obtained from the fusion of mixtures containing a little naphthalene ; usually also 
from pure aqueous solutions. 

They are plates of rhombic outline, having a plane angle of about 72 ; the 
extinction is about 23 with regard to one edge, and about 49 with regard to the 
other. This serves to distinguish the crystals of this modification from the a-crystals, 
which may also appear as rhombs of about 71. 

These crystals melt at about 55 and are, therefore, probably identical with the 
/3- modification of PICKERING. 

y-modification. -If fused monochloracetic acid or the aqueous solution be cooled 
suddenly, the substance crystallises in rhombs having a plane angle of about 59, and 
the plane of the rhomb perpendicular to an acute positive bisectrix. The direction oi 
extinction makes an angle of about 26 with one edge and about 33 with the other. 
The plane of the optic axes is inclined at a small angle (3|) to the shorter diagonal 
of the rhomb ; and the axial angle in air, as determined by an eyepiece micrometer, is 
about 81^. 

These crystals melt at about 50, and are therefore possibly identical with the 
y-modification of PICKERING. Under the microscope the rhombs of y-crystals are 
easily distinguished from those of a-crystals by their plane angle and their extinction ; 
but they may easily be confused with rhombs of y8-crystals lying on the face which 
has a plane angle of about 55 and diagonal extinctions. 

B. Transformations of the Modifications of Monochloracetic Add. 

Transformations of y. When y-crystals which have formed upon a glass slide 
are allowed to stand, they usually become transformed either into /B or into a. If 
they are touched they at once become transformed into ft. In tubes of aqueous 
solution which have been suddenly cooled y-crystals appear, and on shaking become 
transformed into ft, the temperature of the solution rising at the same time to that of 



SPONTANEOUS CRYSTALLISATION OF MONOCHLOKACETIC ACID, ETC. 343 

the freezing-point of ft in that solution. If the tubes are allowed to stand, the 
y-crystals become transformed into with a similar rise of temperature. Sometimes 
they appear to be transformed directly into a, with a rise of temperature to that of 
the freezing-point of a in the given solution. If y-crystals which have been formed 
on a glass slide be inoculated at their margin with a minute fragment of /3, the 
transformation takes place in a very remarkable manner. Crystals of the latter 
modification grow rapidly across the slide from the point of inoculation. They grow 
as single crystals and preserve their orientation quite independently of the orientation 
of the y-crystals, and as they grow they possess a perfectly definite outline showing 
sharp edges just as though they were growing in a liquid. If y-crystals on a slide be 
inoculated at their margin with a fragment of a, a similar transformation takes place 
into , the only difference being that the crystals grow at a much greater speed, so 
that it is more difficult to follow the growth and distinguish the outline of the 
individual crystals. 

Transformation of ft. When ft is crystallised from solution in sealed tubes, it 
is almost impossible to transform it immediately into a, but it is easy to obtain 
^-crystals on a slide either from a drop of solution by friction or from y-crystals by 
merely touching them. The /3-crystals may then be transformed into a by inoculating 
with a small fragment of . Here again the a-crystals grow in the solid ft from the 
point of inoculation in the manner just described, advancing with definite outlines and 
sharp edges. The rate of growth is much slower than when y is directly transformed 
into a. 

C. Aqueous Solutions of Monochloracetic Acid. 

PICKERING (' Journ. Chem. Soc.,' 1895, 67, p. 664) has traced the solubility curves 
for solutions of the three modifications which he calls a, ft, and 8 of monochloracetic 
acid in water ; he gives one point only on the solubility curve of an aqueous solution 
of what he terms y. 

We have therefore investigated aqueous solutions of monochloracetic acid in order 
to determine, if possible, the supersolubility curves for the various modifications of 
the acid described by PICKERING, i.e. the curves which separate the metastable region 
(in which crystals will grow in a supersaturated solution if the solution be inoculated) 
from the labile region (in which crystals will form spontaneously in the solution). 

The aqueous solutions of monochloracetic acid were treated by the methods already 
employed for the various solutions and mixtures for which the supersolubility curves 
have been determined by us, such as sodium nitrate, sodium chlorate, &c. 

Weighed quantities of monochloracetic acid and water were heated together to 
between 80 and 90 in a loosely, stoppered flask, and the heated solution was then 
placed in the trough of the inverted goniometer, described in 'Phil. Trans.,' 1903, A, 
vol. 202, p. 459. A glass prism of known angle and refractive index was immersed in 
the hot solution, and as the solution cooled, the changes in the refractive index of the 



344 



PRINCIPAL HENRY A. MIERS AND MISS FLORENCE ISAAC ON THE 



solution were watched by the method of total reflection within the prism. About 
half of the experiments were made with the smaller goniometer which was used in all 
the earlier work referred to above, but in the remainder of the experiments the acid 
solutions were examined by means of a new inverted goniometer (fig. 4), specially 




Fig. 4. 

designed for this work, the trough of which contains a much larger quantity of 
solution than the smaller instrument (see ' Journ. Chem. Soc.,' 1908, 93, p. 385, where 
this goniometer is briefly described, and the method of regulating the temperature of 
the solution by a stream of hot or cold water flowing over the outer surface of the 
trough is explained) The first step in the present investigation was to plot on the 



SPONTANEOUS CRYSTALLISATION OF MONOCHLORACETIC ACID, ETC. 345 

concentration-temperature diagram the lines of constant refractive index in order to 
interpret the refractive indices in terms of concentration. 

Seven aqueous solutions of known strength were therefore made up, the concentration 
of the monochloracetic acid varying from 83 to 90 per cent. The index of these 
solutions was carefully noted as they cooled from about 50 till crystals first began to 
separate from them, the solutions being stirred steadily throughout the cooling. Until 
crystals began to form, the concentration of each solution was very approximately 
constant during its cooling ; it is, therefore, possible from these experiments to plot 
on the concentration-temperature diagram lines of constant refractive index, each 
experiment giving one point on eacli constant-index line as the temperature falls. 
These constant-index lines were plotted for the following values : 1'422, 1'4'24, 1 '426, 
&c., up to 1'434. They were found to be very approximately straight lines parallel to, 
and equidistant from, each other. On the scale chosen for the diagram, in which 5 
temperature corresponds to 2 per cent, concentration, these lines of constant refractive 
index are inclined at an angle of 40 15' to the temperature axis. 

These lines having been fixed, it is now possible to plot on the diagram by means of 
them the changes in index of any monochloracetic .acid solution as it cools, the 
ordinates giving at the same time the changes in concentration. The solubility curves 
for solutions of the - and ft- modifications, as determined by PICKERING, are also shown 
plotted on the diagram (figs. 5 and 6). 

Solutions giving an a-shower. In the first example (experiment 11) the concentra- 
tion of the acid was approximately 88 per cent. The solution was warmed to about 70 
to dissolve the crystals, and placed in the trough of the smaller inverted goniometer. 
The glass prism was immersed in the solution and the changes in the refractive index 
were watched by the motion of the shadow denoting total reflection. The solution 
was stirred steadily throughout the experiment by a small platinum vane driven by 
an electric motor. The index rose steadily from 1'423981 at 50 to 1 '433359 at 27, 
and no crystals appeared in the solution. At 27 a dense shower of crystals suddenly 
occurred, causing a fall of index to 1 '430377 at this temperature. The crystals were 
examined under the microscope and found to be characteristic a-needles with a plane 
angle of 43 and extinction parallel to the oblique end. After this shower the 
temperature began to fall again, and the index also continued to fall, though much 
more slowly, till it reached 1 '429580 at 29?. This point coincides with the solubility 
curve for a, and the index-temperature curve continues to coincide with the a-solubility 
curve and follows it down the diagram till it reaches 1 '427590 at 17. This experiment 
is an example of a solution giving a spontaneous shower of the a-crystals at the labile 
temperature and fixes a point on the supersolubility curve for the a-modification. 

Solutions giving a /3-shoiver. -In the second example (experiment 24) the concentra- 
tion of the acid was 8 9 '968 per cent. The solution was warmed to about 60 and 
placed in the trough of the smaller inverted goniometer. The solution was stirred 
steadily throughout the experiment. The index rose from 1'429481 at 41 to 

VOL. ccix. A. 2 Y 



346 PKINCIPAL HENEY A. MIERS AND MISS FLORENCE ISAAC ON THE 



00 

on 



Concentration. 

CO 

O 



ID 

tn 



O 
O 




1'436034 at 25, the solution being quite clear of crystals. At 25 a shower of 
crystals occurred suddenly, and the temperature rose to 28, the index falling at the 



SPONTANEOUS CRYSTALLISATION OF MONOCHLOE ACETIC ACID, ETC. 347 

Concentration. 

8 8 8 8 




same time till it reached T433260 at 28. The crystals of this shower were examined 
under the microscope and found to be rhombs of /8, having a plane angle of 71, with 
extinction inclined at about 23 to one side of the rhomb, and the usual interference 

2 Y 2 



348 PRINCIPAL HENRY A. MIERS AND MISS FLORENCE ISAAC ON THE 

figure. After the index had fallen to 1 '433260 at 28, another, much denser, shower 
occurred at this temperature quite suddenly, the temperature rising immediately to 
32. The crystals were now found to have been transformed, and under the 
microscope no /3-crystals were to be seen, but only long a-needles having an angle of 
43 and extinction parallel to the oblique end. The shower of a-crystals rendered 
the solution quite opaque and solid, arid no further readings were possible. At 25 
therefore the solution apparently passed into the labile state for the modification ft. 
At this temperature a shower of /3-crystals appears, and the figure shows the 
concentration to fall somewhat and approach the solubility curve for ft. At 28 the 
solution is within 12 of the /3-solubility curve, and here the much denser shower of 
a-crystals takes place, owing to the fact that although the solution is now metastable 
with regard to ft it is still labile with regard to a. This second shower causes the 
concentration to fall still further, and had not the density of the shower rendered the 
whole solution almost solid and prevented further readings for the index, it would 
doubtless have been possible to trace the index-temperature curve down to the point 
where it touches the solubility curve for a. The shower of /3-crystals in this 
experiment was not nearly so dense as the a-shower, but this is probably due to the 
positions of the solubility curves for a and ft, which show that at any given 
temperature a supersaturated solution is much more strongly supersaturated with 
respect to a than with respect to ft. 

In another solution (experiment 26) the concentration of the acid was again 
approximately 88 per cent,, as in the first experiment. It was also heated to 70 and 
placed in the trough of the smaller goniometer. The index rose from 1 '422974 at 
53 to 1-435442 at 21'5, and no crystals appeared as the solution cooled. From 50 
to 27 the index-temperature curve for the solution practically coincides with that of 
the first experiment described. At 21'5, however, a dense shower of /3-crystals, with 
the usual plane angle and extinction, suddenly occurred. During the shower the 
temperature rose to 25 and the index fell to 1 '432862. The temperature then began 
to fall again, but the index continued to fall, reaching 1 '431870 at 22. The index- 
temperature curve is now within 1 of the solubility curve for ft, as may be seen from 
fig. 6, and the concentration lias fallen considerably from its original value. The 
solution was now inoculated with a minute crystal of the a-modification. The effect 
of the inoculation was to cause an immediate transformation of the /3-crystals and 
another" si lower of a-crystals. The crystals are now all the characteristic needles of 
angle 43 and extinction parallel to the oblique end. The temperature rose from 22 
to 24'5, and the index fell rapidly from 1-431870 at 22 to 1-429680 at 24'5. The 
temperature then fell again and the index also continued to fall, reaching 1 '428092 
at 18'5, a point coinciding with the solubility curve for a. Had the solution not 
been inoculated with a, it is possible that the index-temperature curve for the solution 
would have followed the /J-solubility curve down the diagram as the temperature fell. 
Had this been the case, the index at 18'5 would have been approximately T430 



SPONTANEOUS CRYSTALLISATION OF MONOCHLORACETIC ACID, ETC. 349 

instead of T428, the actual value obtained. This solution was also stirred throughout 
the experiment. The index-temperature curve in fig. 6 for this experiment shows 
two distinct breaks at the points where the two showers occurred. 

The last two experiments described are examples of solutions giving a spontaneous 
shower of ^-crystals before giving the spontaneous a-shower of the first experiment. 
As ft is not the stable modification of the acid, we get a further shower and a 
transformation to a. It will be seen that in the last experiment the solution 
becomes labile at 21'5 with respect to /3, and that the maximum index attained 
is 1'435442. In the first experiment described a solution of the same concentration 
gave an a-shower, and became labile for a at 27, the maximum index attained being 
1 '433359. These two experiments suggest, therefore, that on the concentration- 
temperature diagram the supersolubility curve for the /8-modification of mono- 
chloracetic acid lies to the left of the supersolubility curve for the a-modification, 
just as the /3-solubility curve lies to the left of the a-solubility curve. This is 
confirmed by all the later experiments on solutions of different concentrations. 
The later experiments show that in two solutions of equal concentrations a /3-shower 
always takes place at a lower temperature than an a-shower ; and the maximum 
index attained by a solution giving a /8-shower is always greater than that attained 
by a solution of equal concentration which gives an a-shower. 

Solutions giving a y-shower. In a fourth example (experiment 43) it was found 
possible to obtain a labile shower consisting of crystals of the third modification, y. 
The concentration of this solution was 89 - 5 per cent., nearly the same as that in the 
second experiment. It was heated to about 70 and placed in the trough of the 
large goniometer, which contains about four times the quantity of solution held by 
the trough of the smaller goniometer. The solution was stirred extremely slowly as 
it cooled, the stirring being enough to keep the solution from settling in layers, but 
not enough to cause a violent agitation in the liquid. The index rose from 1 '42401 5 
at 54 to 1-438212 at 18 without crystals appearing in the trough. At 17 0< 8, 
however, a shower of transparent glassy-looking crystals formed suddenly and 
continued to grow in thin sheets, adhering to the sides of the trough and the surface 
of the liquid. The temperature rose immediately to 21'5, and the index fell to 
1-435673. It will be shown later that this point really lies on the solubility curve 
for y, although PICKERING'S observations would not lead to this conclusion. The 
crystals of this shower, examined under the microscope, showed the characteristic 
y-rhombs of angle approximately 58, extinction inclined at about 26 to one side of 
the rhomb, and the usual interference figure. After the temperature had risen to 
21'5 there was a slight halt, and it remained constant for a minute. After this halt 
another shower suddenly occurred and a transformation, and the temperature rose 
further to 24 0- 5. The crystals, when now examined, were found to be of the 
^-modification. The density of the shower prevented any more readings for the 
index. This experiment may be compared with experiment 24 described above, in 



350 



PEINCIPAL HENRY A. MIERS AND MISS FLORENCE ISAAC ON THE 



which in a solution of approximately the same concentration a shower of )8-crystals 
appeared at 25, and the maximum index attained was 1 '436034 at that temperature. 
It therefore appears that the supersolubility curve for y on the diagram lies to the 
left of that for /3, just as the supersolubility curve for /3 lies to the left of that for ; 
this is confirmed by all further experiments giving a y-shower. 

In another solution (experiment 37) which gave a y-shower the concentration was 
approximately 97 '2 per cent. This solution was also examined in the trough of the 
large goniometer, and it was at first unstirred and allowed to cool at rest until it had 
passed the labile temperature for the a- and /3-modifications. The index rose from 
1-430178 at 60 to 1 "440742 at 34'5. Stirring was started at 35, and after a few 
minutes a labile shower of the characteristic y-crystals occurred at 34, the temperature 
rising to 42 at once. No further readings for the index were possible owing to the 
density of the shower, but the temperature was constant at 42 for 5 minutes after 
the shower occurred. Then suddenly a transformation to /8 took place and a rise of 
temperature to 48, after which again the temperature was steady for a considerable 
time. The solution was then inoculated with a minute trace of the a-modification, 
which caused an immediate transformation from /3 to a, and a new rise of temperature 
from 48 to 52 -5. 

The three halts in the change of temperature in this experiment, namely, at 42, 
48, 52'5, are probably at points where the index-temperature curves reach the 
solubility curves for y, /3, and a respectively, though it was not possible to prove this 
by a reading for the index at these temperatures. 

The above method was often found successful in obtaining y-showers, namely, to 
cool the solution, without stirring, past the labile temperature for the a- and 
/3-modifications, and then to start stirring as the solution continues to cool below 
these temperatures. Sometimes the stirring causes an a- or /3-shower to come down 
at once, but often the solution continues to cool without crystals appearing until the 
labile temperature for y is reached, when a labile shower of y-crystals occurs, thus 
determining a point on the y-supersolubility curve. 

The following are the results of a large series of experiments on solutions of various 
concentrations : 

I. Solutions first giving a Spontaneous Shower of a-crystals. 
(The solutions were stirred by means of the revolving platinum vane.) 



Experi- 


Concen- 


ment. 


tration. 




per cent. 


1 


99-5 



Remarks. 



The acid was dried in a desiccator before using. It was placed in the trough of the 
large goniometer, the trough being first heated to about 40. The index rose 
from 1-430774 at 66 to 1-436331 at 52. At 52 a dense spontaneous shower 
of a-crystals occurred, the temperature rose to 61, and the whole mass became 
solid. 



SPONTANEOUS CRYSTALLISATION OF MONOCHLORACETIC ACID, ETC. 351 



Experi- 
ment. 


Concen- 
tration. 


2 


per cent. 

98-5 


3 


95-5 


4 


95-3 


5 


95 


6 


94 3 


7 


94 


8 


91-3 


9 


91-3 


10 


89 


11 


88-3 


12 


86-981 


13 


86 



Remarks. 



The index rose from 1-428224 at 70 to 1-437123 at 48-5. A dense shower of 
a-crystals occurred at 48 -5, and the temperature rose to 60. No further 
readings for the index were possible. 

The index rose from 1- 429183 at 57 -5 to 1-435050 at 44. A dense shower of 
a-crystals occurred at 44, the temperature rising to 51 and the index falling. 

The index rose from 1- 427289 at 63 to 1-435148 at 43. A few a-crystals 
appeared at 45 and a dense a-shower occurred at 43. The temperature rose to 
48 and then fell again. At 47 the index had fallen to 1 431969. 

The index rose from 1-428092 at 60 to 1-434851 at 44. At 46 some a-crystals 
were growing in the solution, and a shower occurred at 44. The temperature 
rose to 46 -5 and the index fell to 1 -431275 at this temperature. 

The index rose from 1-425483 at 64 to 1-435838 at 38 '5. Some crystals 
appeared in the solution at 40, and at 38 5 a dense a-shower occurred. The 
temperature rose to 45 and the index fell to 1-43147 at this temperature, 
corresponding to a point on the a-solubility curve. 

The index rose from 1-427891 at 57 to 1-435640 at 38. At 38 a dense 
spontaneous shower of a-crystals occurred, the temperature rising to 44 with fall 
of index. The temperature then fell again and the index continued to fall, 
reaching 1-432068 at 41 -5. 

The index rose from 1 424783 at 57 to 1 435246 at 31 without crystals appearing. 
At 31 a dense shower of a-crystals suddenly occurred, the temperature rising to 
37 -5 with fall of index. The temperature then fell again and the index 
continued to fall, reaching 1 429480 at 25 - 5. 

The index rose from 1-424583 at 57 -5 to 1-434753 at 33. At 33" a dense 
a-shower occurred, the temperature rose to 37 -5 and the index fell. At 37 the 
index was 1-431175. 

The index rose from 1-422675 at 56 to 1-435050 at 26. At 26 a very dense 
a-shower occurred, causing a rise in temperature to 32 and fall in index to 
1-430575. The temperature then fell again and the index continued to fall, 
reaching 1- 429480 at 23. 

The index rose from 1-423981 at 50 to 1 -433359 at 27 without crystals appearing 
in the solution. At 27 a dense shower of a-crystals occurred, the temperature 
rising to 31 '5 and the index falling suddenly to 1-430377. The temperature 
then fell again and the index continued to fall more slowly, reaching 1-427590 
at 17. From 29 to 17 the index-temperature curve practically coincides with 
the a-solubility curve. 

The index rose from 1-423579 at 47 -5 to T 432666 at 24. No crystals appeared 
till at 23 a dense shower of a-crystals occurred and the temperature rose to 39. 
No further readings for the index were possible owing to the density of the 
shower. 

The index rose from 1-419860 at 54 to 1-433160 at 21-5. At 21-5 a dense 
shower of a-crystals occurred, the temperature rose to 27 and the index fell 
rapidly to 1-429580, a point almost coincident with the a-solubility curve. The 
temperature then fell again, the index continuing to fall so that the index- 
temperature curve from 27 to 18 is practically coincident with the a-solubility 
curve. 



352 PRINCIPAL HENRY A. MIERS AND MISS FLORENCE ISAAC ON THE 



Experi- 
ment. 



Concen- 
tration. 



Remarks. 



14 



15 



16 



per cent. 

85-5 



84-933 



84-5 



17 



82 988 



The index rose from 1-421368 at 50 to 1-433160 at 20. A dense shower of 
a-crystals occurred at 20 and the temperature rose to 25 -5, the index falling 
rapidly to 1-429183, corresponding to a point on the solubility curve for a. The 
temperature then fell again and the index also continued to fall. 

The index rose from 1-424081 at 41 -5 to 1-433260 at 19, no crystals having 
appeared in the solution. At 18 -5 a dense shower of a-crystals occurred, 
causing a rise in temperature to 24. No further readings for the index were 
possible. 

The index rose from 1-421066 at 46'5 to 1-432862 at 18. At 18 a single 
a crystal appeared in the solution, and at 17 -8 an opaque shower of a-crystals 
occurred, the temperature rising to 23 and the index falling very suddenly to 
1-428589. The temperature then fell again and the index rose slightly, but 
finally fell to 1-428390 at 19', corresponding to a point on the a-solubility curve. 

The index rose from 1-4201G2 at 45 to 1-432367 at 14-5. At 14 -5 a single 
long a-needle grow up from the bottom of the solution and a shower of a-crystals 
followed. The temperature rose to 19 and the index fell to 1- 427892. The 
temperature then fell again and the index rose slightly, reaching 1 428192 at 18, 



this corresponding to a point on the solubility curve for a. 



The actual readings are plotted on fig. o and show that at the points where the solutions 
attain their highest index all the index -temperature curves for the various experiments 
very approximately touch a curve parallel to the solubility curve for the a-modification. 
This is the a-supersolubility curve for the aqueous solutions, and is separated from 
the a-solubility curve by an interval of about 9 of temperature. From 82'5 per cent. 
to 88 per cent, of the acid the index-temperature curves give points lying more 
consistently on a continuous curve than in more concentrated solutions. At higher 
points the figure shows the behaviour of the solutions to be more irregular. These 
stronger solutions do not seem to give a-showers so readily as those with concentration 
below 88 per cent., the majority of the solutions examined with concentration above 
88 per cent, giving /3-showers. It will be seen from fig. 5 that in some of the 
experiments, such as 9 and 10, the index-temperature curves have crossed the super- 
solubility curve slightly. It is possible that these solutions became inoculated with 
a at these temperatures and the inoculation caused the labile a-showers, but had this 
not occurred these solutions might have yielded /J-showers and given points on the 
/3-supersolubility curve. The effect of inoculation with a-crystals even at high 
temperatures is very marked. In an inoculated solution the index-temperature curve 
usually fails to reach the supersolubility curve, but as soon as it reaches the solubility 
curve a dense shower occurs, and it continues to follow the solubility curve down the 
diagram as the solution cools. In fig. 5 the a-solubility curve is plotted from 
PICKERING'S results. 



SPONTANEOUS CRYSTALLISATION OF MONOCHLOR ACETIC ACID, ETC. 353 



II. Solutions first giving ^-showers. 
(The solutions were stirred, as before, with the platinum vane.) 



Experi- 
ment. 


Concen- 
tration. 


Remarks. 




per cent. 




18 


99-5 


The acid was dried in a desiccator. The large goniometer was used and the trough 






heated to 40 before introducing the acid. The index rose from 1 '430277 at G6 






to 1 436628 at 49 -5. /3-crystals appeared at 51, and a dense /i-shower occurred 






at 49 - 5, causing the acid to become quite solid and the temperature to rise 






to 55. 


19 


98 


The index rose from 1-429878 at 63 to T 437321 at 45 -5. A few ^-crystals 






appeared at 49" and a shower of /^-crystals at 45 5 ; the temperature rose to 50" 5 






and the index fell to 1 434951, corresponding to a point on the y3-solubility curve. 






The temperature then fell again and the index rose slightly, reaching 1 435050 






at 49 -5. At 49 '5 the temperature rose suddenly to 55, with a transformation 






of /3 into a-crystals. 


20 


95-2 


The index rose from 1 428092 at 61 to 1 438410 at 35 5. At 35" 5 a very dense 






/3-shower suddenly occurred; the temperature rose to 41 '5 and the index fell to 






1 434652. The temperature then fell again and the index continued to fall, 






reaching ! 434354 at 38. On inoculating with a the temperature rose again to 






42", but no more readings for the index were possible. 


21 


94-6 


The index rose from 1-429480 at 57 to 1 -437519 at 36". At 36 a dense shower 






of /^-crystals occurred ; the temperature rose to 40 and the index fell to 1 -434652. 






The temperature then fell again and the index continued to fall, reaching 






1 "432764 at 38 -5 ; this corresponds to a point on the /8-solubility curve. 


22 


92-3 


The index rose from 1-424883 at 61 to 1-437915 at 28. A dense shower of 






/^-crystals occurred at 28 ; the temperature rose to 33 and the index fell to 






1 -435050. No further readings for the index were possible owing to the density 






of the shower, but the temperature fell from 33 to 30, and then rose again 






suddenly from 30 to 34, with transformation of /3 into a. 


23 


90-6 


The index rose from 1 -427690 at 48 to 1-436925 at 26. A shower of /3-crystals 






occurred at 26 and the temperature rose to 29, the index falling to 1 '435050. 






The temperature then fell again and the index fell also, reaching 1-433558 






at 28 -5. 


24 


89 968 


The index rose from 1-429481 at 41 to 1-436034 at 25. At 24-5 a shower of 






/^-crystals occurred ; the temperature rose to 28 and the index fell to 1 -433260. 






The index-temperature curve is here within 2 of the /3-solubility curve. At 28 






another dense shower occurred and the temperature rose immediately to 32. 






The crystals were found to have transformed to a., the solution was opaque 






throughout, and no more readings for the index were possible. 


25 


88-3 


The index rose from 1-424381 at 50 to 1-434951 at 23. At 23 a shower of 






^-crystals suddenly occurred, the temperature rose to 27 and the index fell 






suddenly to 1 432367. The temperature then fell again and the index continued 






to fall, though now more slowly, reaching 1 "431771 at 25 "5, and giving a point 






practically on the solubility curve for ft. No further readings were possible ; the 






crystals were stable for a long time, and at 24 the solution was inoculated with a. 






This caused a transformation from /3 to a and a rise of temperature from 24 






to 26. 


VOL. CCIX. A. 2 Z 



354 PEINCIPAL HENRY A. MIERS AND MISS FLORENCE ISAAC ON THE 



Experi- 
ment. 


Concen- 
tration. 


26 


per cent. 
88-1 


27 


88 


28 


86 


29 


86 


30 


84-8 


31 


84-2 



Remarks. 



The index rose from 1 -422974 at 53 to 1-435442 at 21 -5. A very dense shower 
of /3-crystals occurred suddenly at 21 -5, the temperature rose to 25, and the 
index fell to 1-432862. The temperature then fell again, and the index con- 
tinued to fall, reaching 1-431870 at 22. The solution was now inoculated with 
a and a transformation from /3 to a. took place immediately, the temperature 
rising to 24 -5, with another dense shower. The index fell to 1-429680 at 
24 -5. The temperature fell again, and from 24 -5 to 18 -5 the index-tempe- 
rature curve coincides with the a-solubility curve, the index being 1 428092 at 
18-5. 

The index rose from 1-426183 at 44 to 1-435739 at 21. A single /3-crystal 
appeared at 21, followed at once by a shower of /3-crystals ; the temperature rose 
to 24 and the index fell to 1-433061. The temperature then fell again and the 
index also continued to fall, reaching 1-431969 at 20 -5. Here the temperature 
suddenly rose spontaneously to 23, and the /3-crystals transformed to a. 

The index rose from 1-422675 at 48 to 1-433757 at 19 -5. /3-crystals Appeared 
at 20 and a /3-shower occurred at 19 '5, the temperature rising to 20 and the 
index falling to 1-432466. The temperature then fell again and the index con- 
tinued to fall, reaching 1- 429780 at 13, corresponding to a point on the /3- 
solubility curve. Inoculation with a caused another shower and transformation 
from /3 to a, with rise of temperature from 13 to 16. The index at the same 
time fell to 1-427694 at 16, corresponding to a point on the a-solubility curve. 

The index rose from 1-423177 at 46 to 1-434453 at 17 -9. A few small /3- 
crystals appeared at 19 and a dense shower of ft at 17 -9. The temperature 
rose to 21" and the index fell to 1-432168. The temperature then fell again and 
the index continued to fall, reaching 1-431175 at 19; this corresponds to a 
point, practically, on the /3-solubility curve. 

The index rose from 1-423478 at 42 -5 to 1-434354 at 15. At 15 a very dense 
shower of /3-crystals occurred, the temperature rose to 19, the index falling to 
1-431474. The temperature then fell again and the index continued to fall, 
reaching 1-429978 at 13. After the shower the index-temperature curve coin- 
cides with the /3-solubility curve, from 18 to 13. Two hours later, on inocu- 
lating with a, the whole solution transformed from /3 to a, and the temperature 
rose from 13 to 16. 

The index rose from 1-421872 at 45 to 1-434055 at 13. At 13 a dense /3- 
shower occurred, the temperature rose to 17 -5 and the index fell to 1-430774 
at this temperature, corresponding to a point on the /3-solubility curve. The 
/3-crystals were stable for several hours, but the next day they had transformed 

to a. 



The details of all these experiments are plotted on fig. 6. Here again it will be 
seen that at the points where the solutions attain their highest index the majority of 
the index-temperature curves very approximately touch a curve parallel to the 
solubility curve for the /3-modification. Of the fourteen curves representing the 
above experiments which appear on fig. 6 only four, ranging in concentration from 
9 5 '2 per cent, to 90 '6 per cent., do not behave in this way. In these experiments 
the curves cross the supersolubility curve by from 2 to 4 '5 of temperature and 
therefore pass appreciably into the labile region. These solutions may not have been 



SPONTANEOUS CRYSTALLISATION OF MONOCHLORACETIC ACID, ETC. 355 

sufficiently stirred to bring down the showers at the labile point. After reaching the 
highest index a shower of /3-crystals occurs and all the curves drop towards the 
/3-solubility curve. Unless a transformation from y8 to a takes place, the index- 
temperature curves do not again cross the y8-solubility curve, but continue to coincide 
with it as the temperature falls. If, however, a transformation takes place, the 
temperature rises at once, and the concentration and index drop till the index- 
temperature curves touch the a-solubility curve. This behaviour is shown in fig. 6 
by experiments 26 and 28. In several of the other experiments, also, transformation 
takes place, either spontaneously or by inoculation, but it was not possible to obtain 
readings for the index owing to the density of the shower. The rise of temperature, 
however, always showed that the index-temperature curve had fallen approximately 
to the a-solubility curve after the transformation. 

In experiments 1 and 18 the dried acid was melted and used in the trough of the 
larger goniometer without adding any water. The acid, however, is so hygroscopic 
that it probably always picks up a little water during the experiment. This difficulty 
of keeping the concentration constant recurs throughout, even in the preliminary 
experiments which fix the lines of constant index. An attempt to keep the solutions 
covered with oil was not successful owing to the oil mixing very readily with the 
acid. It is probable, therefore, that some small inaccuracy results from this cause 
throughout the whole series of experiments, though it is more marked as the 
concentration becomes higher. 

The /3-crystals were sometimes found to be stable for a considerable time, and in 
some experiments they remained withoxit transforming for many hours. The solu- 
bility curve for the a- and /S-modifications of the acid is plotted on fig. G from the 
values obtained by PICKERING. 

The /3-solubility and supersolubility curves are separated from each other by an 
interval of about 7'5 of temperature, which is slightly less than the interval 
separating the a-solubility and supersolubility curves. 

As has already been noticed, the index-temperature curves of experiments 20, 21, 
22, and 23, in fig. 6, cross the supersolubility curve. In order to ascertain whether it 
is insufficient stirring which causes these solutions to pass somewhat into the labile 
state, two other experiments were made, with the same concentrations as in 
experiments 20 and 21, in which the solutions were stirred more violently. In these 
the stirring was effected by means of a plunging stirrer of glass, shaped like a horse- 
shoe, fitting inside the goniometer trough as shown in fig. 4, and driven by the 
electric motor. This moved rapidly up and down, and kept the whole solution in 
violent motion. The following results were obtained ; 



2 z 2 



356 PRINCIPAL HENRY A. MIERS AND MISS FLORENCE ISAAC ON THE 



Experi- 
ment. 



32 



33 



Concen- 
tration. 



per cent. 

95 



92-2 



Remarks. 



The goniometer trough was heated to 30 before putting in the solution. The index 
rose from 1-432300 at 50 to 1 -437123 at 38. A shower of /8-crystals occurred 
very suddenly at 38, the temperature rising to 42 -5 and the index falling to 
1 434354, when the solution became opaque. 

The trough was again heated to 30 before putting in the solution. The index rose 
from 1 430077 at 46 5 to 1 436265 at 32. At 32 a dense shower of /^-crystals 
occurred very suddenly, the temperature rose to 35 5, and the index fell to 
1-433491. The temperature then fell again, but the density of the shower 
prevented any further readings. On inoculating the solution with a, transforma- 
tion from /3 to a took place, and the temperature rose again from 35 to 39 5. 



The index-temperature curves of these two experiments, at the temperatures at 
which they attain their highest refractive index, give points which lie very 
approximately on the supersolubility curve of fig. 6 as previously determined. We 
may assume, therefore, that in experiments 20, 21, 22, and 23 the stirring was not 
sufficient to bring down the /3-showers on the supersolubility curve, and that the 
solutions therefore passed somewhat into the labile region. 

III. Solutions first giving y-shoivers. 
(In all these experiments the larger goniometer of fig. 4 was used.) 



Experi- 
ment. 


Concen- 
tration. 


Remarks. 


34 
35 

36 
37 


per cent. 

98-5 
98-5 

98-3 
97 


The index rose from 1 -430675 at 64 to 1 '437619 at 47. At 47 a shower of 
y-crystals occurred, and the temperature rose to 49 '5. This solution was stirred 
gently throughout the experiment, and becomes labile with regard to a. at 50 5 
and with regard to /? at 49. 

The trough was heated to 40 before introducing the solution, which was at first 
unstirred. The index rose from 1-431241 at 62 to 1-437156 at 48, stirring 
being started at 49. Crystals began to grow at the bottom of the trough at 48, 
and a y-shower took place which was not very dense. The temperature rose to 
49 and was then stationary. Later a transformation from y to /3 took place, with 
a rise of temperature to 54. 

The trough was heated to 50 before introducing the solution, which was not stirred 
until it had cooled to 49. The index rose from 1 430675 at 61 to 1 436829 at 
47 -5. At 47 -5 a shower of y-crystals occurred, the temperature rose to 49 
and was then stationary. After a time a further rise of temperature to 54 
occurred, with transformation of the y-crystals to p. 

This solution was also unstirred until the temperature had fallen to 34 -5. The 
index rose from 1-430178 at 60 to 1-440742 at 34 -5. A dense shower of 
y-crystals occurred at 34, the temperature rose to 42 and was then stationary. 
After 5 minutes a transformation to ft took place, with a rise of temperature to 
48. On inoculation with a, a further transformation from /? to a took place, 
and a rise of temperature to 52 5. 



SPONTANEOUS CRYSTALLISATION OF MONOCHLORACETIC ACID, ETC. 357 



Experi- 
ment. 


Concen- 
tration. 


Remarks. 




per cent. 




38 


96-5 


The index rose from 1-430011 at 58 to 1-440610 at 32-5. Stirring was first 






started at 33, and a y-shower took place at 32 5, the temperature rose to nearly 






40 and was stationary for 5 minutes. On again stirring gently, transformation 






to p took place, the temperature rising to 45. On inoculating with a., a further 






transformation from ft to a took place, and the temperature rose to 50. 


39 


95-8 


This solution was unstirred till the temperature had fallen to 34. The index rose 






from 1-428257 at 60 to 1-440283 at 32 -5. A shower of y-crystals occurred at 






32 5, the temperature rising to 38, when it was stationary. After 5 minutes a 






transformation to /? took place and the temperature rose to 45. 


40 


94 


This solution was unstirred till the temperature had fallen to 28. The index rose 






from 1-428722 at 55 to 1-440085 at 27. At 27 a shower of y-crystals 






occurred, the temperature rose to 31 and was stationary. After a few minutes 






transformation to ft took place, with rise of temperature to 37. 


41 


93 


This solution was unstirred till the temperature had fallen to 27. The index rose 






from 1-425934 at 60 to 1-439697 at 26. On stirring slightly from 27 a 






shower of y-crystals occurred at 26. While- the y-crystals were yet growing a 






transformation into /^-crystals took place, with a rise of temperature from 26 






to 37. 


42 


92-7 


This solution was also unstirred. The index rose from 1 -423311 at 64 to 1 '441067 






at 21'5. At 21'5 y-crystals shot suddenly through the whole solution and the 






temperature rose to 27 -5. On now stirring slightly, transformation from y to j8 






occurred, with a rise of temperature from 27 "5 to 35 1. On inoculating with a, 






a further transformation from ft to a occurred, with a rise of temperature from 






35 to 38. 


43 


89-5 


This solution was stirred gently throughout the experiment. The index rose from 






1-424015 at 54 to 1-438212 at 18. At 17- 8 a shower of y-crystals occurred; 






the temperature rose to 21-5 and the index fell to 1 -435673. The temperature 






remained constant at 21 -5 for a short time, and then rose suddenly to 24 '5, 






with transformation from y to (3. 


44 


89-5 


This solution was stirred throughout. The index rose from 1-422038 at 60 to 






1 -437882 at 19 -5. At 19 -5 a shower of y-crystals suddenly occurred, the index 






fell, and the temperature rose slightly. 


45 


89 


This solution was also stirred throughout. Cold water was passed over the sides of 






the trough as the solution cooled from 30 to 20, so that the cooling was very 






rapid over the period where an a, or /3 labile shower might be expected. The 






index rose from 1-426520 at 47'5 to 1-438311 at 17-5. At 17-5 a shower of 






y-crystals occurred, but no appreciable rise of temperature took place. After 






3 minutes a transformation to f3 took place, with rise of temperature to 24, the 






index falling to 1 434057 at this temperature. The temperature then fell again 






and the index continued to fall, reaching 1 -430642 at 19 ; this corresponds to a 






point on the /8-solubility curve. 



The details of these twelve experiments, in which the solutions give y-showers, 
appear on fig. 7. Here also it will be seen that at points where the index-temperature 
curves attain their highest values they all approximately touch a continuous curve, 
the supersolubility curve for y. The y-solubility curve also appears ou fig. 7, and is 



358 PRINCIPAL HENEY A. MIEES AND MISS FLOEENCE ISAAC ON THE 

8 



Concentration. 

8 



to 

en 




plotted from values obtained later in this paper. For lower values of concentration 
the y-supersolubility curve is approximately parallel to the y-solubility curve, but 



SPONTANEOUS CRYSTALLISATION OF MONOCHLOR ACETIC ACID, ETC. 359 

with higher concentration, such as from 98 to 100 per cent., it appears to bend round 
and practically meet the y- solubility curve. For these higher concentrations it 
therefore appears that the y-solutions hardly supersaturate at all. 

In the trough the shower of y-crystals grew quickly in sheets, adhering to the prism 
and sides of the trough, thus making further readings for the index difficult. In only 
a few instances was the stirring continued right through the experiment, for it was 
generally found that when the stirring was constant throughout cooling, either an a- 
or ^8-shower occurred, and not a y-shower. In experiment 42 the solution was not 
stirred at all until after the y-shower had been obtained, and it will be seen from 
fig. 7 that the index-temperature curve for this experiment consequently crosses the 
y-supersolubility curve somewhat and passes into the labile state for y. 



IV. Motwchloracetic Acid (nearly pure] stirred in an open Beaker at Higher 

Temperatures. 

* 

In the above experiments the solutions containing from 98 per cent, to 100 per cent. 
of the acid crystallise spontaneously at comparatively high temperatures, i.e. from 
about 46 to 52'5 for the various modifications of the acid. 

Since it is not very convenient to work at and above these temperatures in the 
goniometer trough owing to the fumes from the acid which attack the metal of the 
goniometer slightly, a few additional experiments were undertaken in which the acid 
was heated to between 70 and 80 and stirred in a small open beaker as it cooled. 
The temperatures at which the various showers occurred were noted, and the stirring 
was again effected by means of the small revolving platinum stirrer. 

The acid was taken direct from the bottle and no water was added. Previous 
experiments on the refractive index show that the acid, unless carefully dried for 
some days in a desiccator, nearly always contains from 1 per cent, to 1 '5 per cent, of 
water, so that the concentration of the acid used may be regarded to be from 
98 '5 per cent, to 99 per cent., unless previously dried, when it is probably about 
9 9 - 5 per cent. The following results were obtained : 



1. a-shower. 



Approximate 
concentration of 
acid. 


Temperature 
of 
crystallisation. 


Temperature to which 
solution rose during 
crystallisation. 


per cent. 

99-5 


52 




61 



360 PEINCIPAL HENEY A. MIERS AND MISS FLOKENCE ISAAC ON THE 

2. fi-showers. 







Approximate 
concentration of 


Temperature 
of 


Temperature to which 
solution rose during 


acid. 


crystallisation. 


crystallisation. 


per cent. 


. 


_ 


98-5 


49 


55-5 


99-5 


50 


55-5 


99-5 


49 


55 


99 


48-5 


55 


99-5 


48-5 


56 


99 


50 


55-5 


99 


50 


55-5 



3. y -showers. 



Approximate 


Temperature Temperature to which 


concentration of 


of solution rose during 


acid. 


crystallisation. 


crystallisation. 


per cent. 


. 


o 


99 


4G-5 


50 


99-5 


47 


50 


99 


40-5 


50 


99-5 


47 


50 



In some of these experiments the acid appears to become inoculated at the edges of 
the beaker a short time before the shower occurs, and this may bring the shower down 
a little too early, but the general results here obtained give points lying very 
approximately on the supersolubility curves already determined by the previous 
experiments on the refractive indices. 



V. Verification of the Supersolubility Curves by Experiments witli Sealed Tubes. 

In order to verify the three supersolubility curves obtained above for the three 
modifications of monochloracetic acid a, ft, and y, another series of experiments was 
undertaken in which aqueous solutions of the acid of various concentrations were 
enclosed in sealed tubes and heated in water to about 80 until all the crystals had 
dissolved. The tubes were then allowed to cool very gradually in a large beaker aud 
were attached to glass rods, by means of which they could be shaken by hand as they 
cooled. They were always shaken violently throughout the whole process of cooling, 
and the temperature at which crystals first formed in a tube was noted for each tube 
in turn. The crystals which formed were immediately examined under the microscope 
in order to ascertain which modification had separated. 



SPONTANEOUS CRYSTALLISATION OP MONOCHLORACETIC ACID, ETC. 361 

Sometimes a separates and sometimes y, but most generally ft ; this was also found 
in the trough experiments on the refractive indices. It is, however, impossible 
to predict with any certainty which modification will separate from any given 
tube. 

Showers of a-crystals were not at all general, but were obtained more frequently in 
tubes containing from 86 per cent, to 88 per cent, of acid than in tubes of higher 
concentrations, and usually when a solution in any tube first crystallised as a it 
continued to do so again and again, even though heated several times in boiling 
water for various lengths of time to dissolve the crystals. This suggests that a 
particular modification may exist even in the liquid state and that it is ready to 
crystallise as soon as the labile temperature is reached. Similarly, if a tube had first 
crystallised in a /3-shower, it usually continued to give /3-showers when heated again 
to dissolve the crystals and then recooled. The above statement does not invariably 
hold good, however, for occasionally a tube was found to give both a- and /3-showers 
in turn after successive heatings and coolings. Friction generally has a special 
effect in bringing down /3-showers, in fact /B appears to be far the most usual 
modification to crystallise in the tubes. It was found that when only a few glass 
fragments were enclosed in the tubes to produce friction the /3-showers did not 
usually occur until the solutions had passed into the labile state by about 3 of 
temperature and, therefore, crossed the supersolubility curve defined by the experi- 
ments on refractive indices. If, however, a few fragments of some heavier material 
such as corundum or tinstone were enclosed in the tubes to produce the friction, the 
/3-showers were found to occur as soon as the sohition had reached the labile 
temperature. Showers of y-crystals usually occurred in tubes containing glass 
fragments when the solutions have cooled below the labile temperature for a and ft 
without crystallising. As has been mentioned previously, when y-cvystals are 
slightly agitated they at once transform to ft. The same was found with the 
y-crystals in the tubes, for if they are shaken in the solution they at once transform 
to ft. Occasionally, when a tube gave a shower at the y labile temperature, it was 
found on examination that the crystals were of the /^-modification. There is little 
doubt, however, in these cases that the shower first started as y-crystals and that the 
shaking transformed them at once into ft. 

The tubes were all heated in hot water, to dissolve the crystals, to temperatures 
varying from 50 to 100, and for lengths of time varying from five minutes to one 
hour, but neither the length of time nor the temperatures to which the solutions are 
heated appear to have any effect on the temperature of crystallisation. 

The results of the experiments with tubes are tabulated below ; some tubes 
contained glass fragments, some corundum, and some tinstone. 

The eight a-points, if plotted on the concentration-temperature diagram of fig. 5, will 
be seen, in general, to lie not far from the supersolubility curve. Some of the points 
are from 0'5 to 1'5 to the left of the a-supersolubility curve These tubes have 

YQL. CCIX. 4, 3 A 



362 PEINCIPAL HENRY A. MIEKS AND MISS FLORENCE ISAAC ON THE 



1. Tubes giving a-showers. 









Labile temperature 


Experiment. 


Concentration of acid. 


Temperature of crystallisation. 


as shown by the 
supersolubility curve. 




per cent. 





> 


46 


99 '5 with glass 


52 


52 


47 


98-5 


51, 49, 48-5 


49 


48 


92-68 


36 


35-5 


49 


90 '1 corundum 


28, 28, 28 


29-5 


50 


88-477 glass 


25, 28-5, 28-5, 28-5, 26'5 


26-5 


51 


88-206 ,, tinstone 


25 


25-5 


52 


87 9 1 corundum 


23-5, 22-5 


25 


53 


86-528 


21, 21 


22-3 



therefore passed somewhat into the labile region before crystallising, but this may be 
due to insufficient friction within the tube. 

Experiment 50, with concentration 88'477 per cent., is anomalous, since this 
solution becomes labile at 26 '5 ; yet it crystallised in the tube three times at 28'5 in 
the metastable state. This is the only tube in the whole of this research which 
behaves in this manner, and no explanation was found, unless it be that some error 
may have occurred in weighing the acid and water contained in the tube. 



2. Tubes giving (3-showers. 









Labile temperature 


Experiment. 


Concentration of acid. 


Temperature of crystallisation. 


as shown by the 








supersolubility curve. 




per cent. 








54 


99-5 with glass 


48-5, 50, 49, 50, 50, 49, 48-5 


49-5 


55 


97 569 corundum 


45-5, 46 


45 


56 


96-115 


40-5, 40, 40-5 


41 


57 


95 09 tinstone 


37 


38 


58 


95 04 corundum 


36-5, 36-5, 37 


38 


59 


93-162 


33-5, 34-5, 34-5, 35 


34-5 


60 


91-572 


30, 30 


30-5 


61 


90-1 


27 


27 


,62 


90-034 tinstone 


27 


27 


63 


89 268 corundum 


24-5, 25 


25-5 


64 


87-91 


21, 21, 23 


22-5 


65 


86-528 


18-5 


19-5 



All these points, if plotted on the concentration-temperature diagram of fig. 6, will 
be found to lie almost exactly on the ^-supersolubility curve plotted from the results 
of the refractive index experiments. The tube experiments, therefore, completely 



SPONTANEOUS CRYSTALLISATION OF MONOCHLOEACETIC ACID, ETC. 363 



verify the super solubility curve by an independent method. It is evident that glass 
fragments do not cause sufficient friction in a tube to bring down the /J-shower 
exactly at the labile point. For instance, a tube containing a few glass fragments and 
95'062 per cent, of the acid could not be made to give a /8-shower till the temperature 
had fallen to 35. It is seen from the above table that a tube of the same 
concentration containing corundum or tinstone crystallises at 37. Numerous other 
similar results were obtained in which tubes containing only glass fragments passed 
somewhat into the labile state before giving the showers, but they are omitted in 
the above table. 

3. Tubes giving y-showers. 
(All these tubes contain glass fragments.) 







Labile temperature 


Experiment. 


Concentration of acid. 


Temperature of crystallisation. 


as shown by the 
supersolubility curve. 




per cent. 




. 


66 


99 


45, 46-5, 47, 46-5, 46-5, 47 


47 


67 


97-542 


35, 35-5, 35 


36 


68 


96 


30-8 


32 


69 


95-044 


29, 29 


29-5 


70 


94-113 


26-5, 26-5 


27 


71 


94-11 


26-5, 24-5 


27 


72 


92-68 24-5 


24-5 


73 


92-562 


23-5, 23-5 


24-5 


74 


89-863 


19, 19 


19 


75 


88-477 


16, 16 


16 



If these 10 points be plotted on the concentration-temperature diagram of fig. 7, 
containing the results of the experiments on refractive indices in which y-showers 
were obtained, they will be found to lie very approximately on the y-supersolubility 
curve there shown. These tube experiments may therefore be regarded as confirming 
the y-supersolubility curve obtained by the method of refractive indices. 

4. Outlying Points. During the course of the experiments with solutions enclosed 
in sealed glass tubes with a few glass fragments it was occasionally found that the 
solution failed to crystallise anywhere in the neighbourhood of either of the super- 
solubility curves a, /J, or y, but passed quite into the labile region before crystallising. 
No reason could be assigned for their behaviour, since they were treated in precisely 
the same manner as usual, being heated to between 60 and 80 for various lengths of 
time to dissolve the crystals, and then shaken continually as they cooled in a water 
bath. All the temperatures of crystallisation were, however, recorded, and the 
following are the collected results giving these outlying points in the labile region. 
When examined under the microscope, the crystals proved to be always ft or y. 

3 A 2 



364 PRINCIPAL HENRY A. MIERS AND MISS FLORENCE ISAAC ON THE 



Experiment. 


Concentration of acid. 


Modification. 


Temperature of crystallisation. 




per cent. 







76 


97-542 


7 


31-5 


77 


96 


13 


27 


78 


94-044 


y 


24, 24 


79 92-562 


y 


19, 19 


80 


89-863 


P 


13-5, 14 


81 


88-124 


y 


12 



On plotting these points on the concentration-temperature diagram fig. 8, it will 
be found that they also lie very approximately on a continuous curve to the left-hand 
side of the -, ft-, and y-supersolubility curves, nearly parallel to them, and separated 
from the y-supersolubility curve by between 4 and 5 of temperature. These points 
appear on fig. 8, which also gives all the solubility and supersolubility curves for 
the three modifications. 

It is just possible that these outlying points may give the supersolubility curve 
corresponding to a fourth, very unstable, modification of monochloracetic acid, and 
may correspond to that which PICKERING has called 8. 

No other evidence of its existence has, however, been found, and no sign of a 
fourth modification has ever been seen under the microscope throughout this work ; 
if it exists at all, it is probably so unstable that it transforms instantaneously into 
either y or ft. 

These experiments complete the whole of the results obtained from shaking 
solutions in sealed tubes. 



VI. The Solubility Curves for the Different Modifications of Monochloracetic Acid. 

It has been previously mentioned that PICKERING has determined solubility curves 
for the three modifications of monochloracetic acid which he calls a, ft, and 8, and 
also one point on the solubility curve for the modification which he calls y. In our 
three figs. 5, 6, 7, which give the three supersolubility curves for the modifications a, 
ft, and y of the acid, the three corresponding solubility curves also appear. On 
figs. 5 and 6 the solubility curves for the a- and ^-modifications are plotted from 
PICKERING'S results, but on fig. 7 the solubility curve for the y-modification is plotted 
from the results obtained below. All three solubility curves have, however, been 
obtained independently of PICKERING by a method which has been used before in our 
previous work. 

Weighed quantities of the monochloracetic acid and water were enclosed in sealed 
glass tubes. They were then heated in a water bath until all the acid crystals had 
dissolved, except one or two very small crystals which were preserved at the upper 
end of the tube. The tubes were then allowed to cool gradually in a beaker of water 



SPONTANEOUS CRYSTALLISATION OF MONOCHLORACETIC ACID, ETC. 365 



Concentration. 




366 PEINCIPAL HENRY A. MIEES AND MISS FLORENCE ISAAC ON THE 

and shaken continually while the enclosed crystals were watched with a lens. The 
small crystals appeared to dissolve at first, their edges becoming more and more 
rounded, until the water-bath fell to a certain temperature, after which the crystals 
were seen to grow, their edges becoming quite sharp. This change is quite distinct, 
and the temperature at which it occurs is taken as the temperature of saturation. 
Thus each tube may give three temperatures of saturation at which crystals will 
begin to grow, according as the enclosed crystals are a, /3, or y. 

Each experiment was repeated once or twice and with both rising and falling 
temperatures. The mean of the values obtained was taken as the temperature of 
saturation. 

The following results were obtained : 

1. Points on the a-solubility Curve. 



Experiment. 


Concentration of acid in tube. 


Temperature 


of saturation. 




per cent. 







82 


99 


61 


5 


83 


99 


61 




84 


97-542 


55 




85 


96 


52 


3 


86 


91-672 


42 




87 


86-876 


32 





PICKERING gives six points on the a-solubility curve between the concentrations 
80 per cent, and 100 per cent, of the acid, and the above points agree almost exactly 
with his results. 

2. Points on the ft- solubility Curve. 



Experiment. 


Concentration of acid in tube. 


Temperature of saturation. 




per cent. 





88 


99 


55 


89 


97-542 


50 


90 


96 


47-2 


91 


95-044 


44-5 


92 


94-11 


42-5 


93 


92-562 


38-8 


94 


88-477 


30-8 


95 


86-876 


27-1 



PICKERING also gives six points on the /3-solubility curve between the concen- 
trations 80 per cent, and 100 per cent, of the acid, and here also the points obtained 
above agree almost exactly with his results. 



SPONTANEOUS CRYSTALLISATION OF MONOCHLOEACETIC ACID, ETC. 367 



3. Points on the y-solubility Curve. 



Experiment. 


Concentration of acid in tube. 


Temperature of saturation. 




per cent. 





96 . 


99 


50 


97 


97-542 


43-5 


98 


96 


41 


99 


95-044 


37-5 


100 


94-11 


34-5 


101 


92-562 


30-25 


102 


91-672 


28-5 


103 


88-477 


21-5 


104 


86-83 


17 



The only points obtained by PICKERING on the y-solubility curve are 100 per cent, 
solution saturated at 50, and 96 '02 per cent, solution saturated at 41'4. It may be 
seen that both these points agree fairly well with the above results. 

The above points are found to lie on a continuous curve and give the y-solubility 
curve which appears on figs. 7 and 8. The y-solubility curve runs nearly parallel to 
the y-supersolubility curve, and is separated from it by about 7 of temperature, 
except at the upper end, where the y-solubility and supersolubility curves approach 
each other much more nearly. 

Nothing has been found to correspond to PJCKKKING'S solubility curve for 8. 

VII. Relative Positions of the a-, ft-, and y-solubility and Supersolubility Curves. 

In fig. 8 are plotted all the six curves obtained in this paper, namely, the three 
solubility and three supersolubility curves for the a.-, ft-, and y-modifications of 
monochloracetic acid, as well as a seventh curve formed by the outlying points 
referred to above in this paper. It will be seen from the relative positions of these 
curves that after a y-shower has occurred at the y-supersolubility curve and the 
concentration of the solution has fallen to the y-solubility curve and it has become 
just saturated with respect to y, the solution is always not only supersaturated, but 
labile, with respect to a and ft. Hence only a slight stirring is enough to cause a 
transformation of y into ft or a. without inoculation, and since the ^-supersolubility 
curve is only separated from the y-solubility curve by from 1 to 2 C> 5 of temperature, 
the y-crystals usually transform to ft when agitated. 

On the other hand, of the /8-curves the supersolubility curve lies to the left, and 
the solubility curve to the right, of the a-supersolubility curve. Hence, after a 
spontaneous shower of ft has occurred and the concentration has fallen to the 
/3-solubility curve and the solution has become just saturated with respect to ft, it is 
only metastable with respect to a, and not labile. 

Hence, unless the solution is inoculated with a, the /3-crystals are stable, as has, 



368 PRINCIPAL HENRY A. MIERS AND MISS FLORENCE ISAAC ON THE 

been shown in the above experiments. The positions ojf these curves, therefore, account 
for the relative stability and instability of the ft- and y-crystals respectively. As has 
been shown, a shower of y-crystals in a closed tube always transforms to ft or a on 
shaking the solution, but a /3-shower very rarely transforms to a. 



VIII. Additional Experiments with Pure Monochloracetic Acid, 

All the monochloracetic acid used in these experiments is the ordinary commercial 
acid, and, as has been mentioned, it in all probability contains a little water even 
when it is dried in a desiccator, as it is very hygroscopic. In order to determine the 
true melting-points of the different modifications of the pure dry acid, a few additional 
experiments were made with a small quantity of the acid which had been specially 
purified for this purpose by Mr. NAGEL, to whom we are much indebted for kind 
assistance. 

Experiment 105. The acid was enclosed in five sealed tubes. Two of the tubes 
contained corundum fragments with the acid ; two, glass fragments, and the remaining 
tube contained the pure acid alone. The melting-points of all three modifications, 
a, ft, y, were found in the manner already described, and gave the results : 

Modification. Melting-point. 

............. 62'4, 

ft ............. 56'5, 

y ............. 51. 

The melting-points found above, using the commercial acid, were : 

Modification. Melting-point. 



ft ............. 55, 

7 ............. 50, 

while the corresponding points found by PICKERING were : 

Modification. Melting-point. 



ft ............. 56-01, 

y ............. 50. 

It is, therefore, certain that both the acid used in this research and that used by 
PICKERING contain a little water, and this conclusion is also borne out by the 
experiments 2, 18, 34. 35, &c., on the refractive indices, where the acid was used 



SPONTANEOUS CRYSTALLISATION OP MONOCHLOKACETIC ACID, ETC. 369 

without the addition of water and yet the corresponding index-temperature curves on 
the figs. 5, 6, 7 show the concentration to be between 98 and 99 per cent. 

Experiment 106. The same tubes of pure acid were used to determine the true 
points of spontaneous crystallisation, with the following results. The tubes were 
heated to 70 for various lengths of time to dissolve the crystals : 

a-showers, none. 

yS-showers in tubes containing corundum fragments occurred at 52, 52. 
y-showers in tubes containing glass fragments occurred at 47'4, 47. 
The tube containing the acid alone gave a y-shower at 46'5. 

The corresponding temperatures of spontaneous crystallisation for the three 
modifications obtained above with the commercial acid were : 

a-showers at 52, 
/3-showers at 50, 
y-showers at 47. 

Here also, therefore, the results show that the commercial acid contains some water. 

Although no temperature of spontaneous crystallisation for a. was obtained with 
the pure acid, it is probably above 52, just as the temperature of spontaneous 
crystallisation for /3 with the pure acid was above 50. 

The above experiments with the tubes containing pure acid comprise over a dozen 
different experiments, yet no a-showers were obtained ; this difficulty in obtaining 
a-showers in sealed tubes has been noticed above. 



PART II. MIXTURES OP NAPHTHALENE AND MONOCHLORACETIC ACID. 

Introduction. 

The investigation of monochloracetic acid and its solutions in water being completed, 
and the existence ascertained of the three different solubility and supersolubility 
curves corresponding to the modifications a, ft, and y of the acid, we were able to 
return to the study of the crystallisation of mixtures of naphthalene and mono- 
chloracetic acid, which has already been referred to at the beginning of this paper, 
It was there mentioned that in all probability mixtures of naphthalene and mono- 
chloracetic acid do not form mixed crystals at all, but are only an example of the 
crystallisation of two pure substances from their mixtures. In the long series of 
experiments, of which the account is given below, there has never been any indication 
of the formation of mixed crystals. A large number of mixtures were made up, 
varying in concentration from 100 per cent, naphthalene per cent, monochloracetic 
acid to per cent, naphthalene 100 per cent, monoohloracetic acid, and enclosed in 

VOL. ccix. A, 3 B 



370 PRINCIPAL HENRY A. MIERS AND MISS FLORENCE ISAAC ON THE 

sealed tubes and their melting- and freezing-points carefully determined. But in no 
case was there found to be any appreciable difference in temperature between these 
points, each mixture both melting and freezing at one definite temperature. CADY'S 
results referred to above, p. 338, are, therefore, not confirmed by our experiments, for 
although we have obtained a solubility curve for mixtures of naphthalene and mono- 
chloracetic acid agreeing very approximately with the freezing-point curve obtained 
by him, we have been able to obtain no evidence whatever of the existence of his 
melting-point curve. 

We may assume, therefore, that mixed crystals are not formed from mixtures of 
monochloracetic acid and naphthalene, and a study of the crystallisation of these 
mixtures will, therefore, yield results similar to those already obtained for mixtures 
of salol and betol ('Roy. Soc. Proc.,' A, 79, 1907), the only new feature being 
introduced by the existence of the three modifications of monochloracetic acid. 



I. The Solubility Curves. 

In the experiments to determine the solubility curves for mixtures of mono- 
chloracetic acid and naphthalene the mixtures of various concentration were weighed 
carefully and enclosed in sealed glass tubes, the acid being dried in a desiccator for 
several days before being used. 

The method of finding the freezing- or melting-point for each mixture was precisely 
the same as that employed for the aqueous solutions, p. 3G4. Each tube was heated 
in a water-bath until all the enclosed crystals had melted, with the exception of one 
or two very small crystals at the top or bottom of the tube. The tubes were then 
allowed to cool gradually in the water- bath and shaken continually while the enclosed 
crystals were watched with a lens. The temperature at which the crystals began to 
grow, as shown by their edges becoming sharp, was taken to be the freezing-point. 
Similarly, with rising temperature, the point at which the few small crystals first 
begin to lose their sharp outline is taken as the melting-point. In no case did the 
freezing-point for any mixture vary by more than 0'5 from the melting-point, and 
the mean of the two is taken as the true temperature of saturation. In a few cases 
the mixture was placed in an open tube, which was firmly closed with a rubber 
stopper, and the mixture was inoculated with a minute fragment of the crystal 
required. The melting- and freezing-points were obtained in exactly the same way 
by observing the behaviour of the small introduced crystal. Theoretically, each tube 
may give four temperatures of saturation, according as the enclosed crystals are 
naphthalene or either the a-, /3-, or y-modification of the acid, and practically all four 
temperatures have been ascertained in more than one mixture. 

Each experiment was repeated several times, both with rising and falling tem- 
peratures, and the following are the final results obtained : 



SPONTANEOUS CRYSTALLISATION OF MONOCHLORACETIC ACID, ETC. 
1. Solubility of Naphthalene in Monochloracetic Add. 



371 



Experiment. 


Concentration of naphthalene 
in mixture. 


Temperature of saturation. 




per cent. 


. 


107 


100 


79-5 


108 


88-922 


75-5 


109 


80 


72-5 


110 


69-7 


69-5 


111 


60 


66-5 


112 


50-02 


62-5 


113 


40-035 


58-75 


114 


35 


55-5 


115 


30-04 


52-5 


116 


23-27 


47-5 


117 


23 


47-5 


118 


20 


45-5 


119 


15 


43-5 



2. Solubility of the a-modification of Monochloracetic Acid in Naphthalene. 



Experiment. 


Concentration of acid in 
mixture. 


Temperature of saturation. 




per cent. 


. 


120 


100 


61-5 


121 


90-049 


58 


122 


85-297 


56-5 


123 


84-974 


56-8 


124 


80-06 


55 6 


125 


80-085 


55-6 


126 


78 


55 


127 


77-015 


54-5 


128 


77 


54-5 


129 


76-73 


54 


130 


70 


53 


131 


65 


52 


132 


60 


50-5 



3. Solubility of the ^-modification of Monochloracetic Acid in 



Experiment. 


Concentration of acid in 
mixture. 


Temperature of saturation. 




per cent. 





133 


100 


55 


134 


90-049 


52 


135 


85-297 


50-5 


136 


80-06 


50-1 


137 


78 


50 


138 


77-015 


49-8 


139 


70-5 


48-5 



3 B * 



372 PRINCIPAL HENRY A. MIERS AND MISS FLORENCE ISAAC ON THE 
4. Solubility of the y -modification of MonocUoracetic Acid in Naphthalene* 



Experiment. 


Concentration of acid in 
mixture. 


Temperature of saturation 




per cent. 





140 


100 


50 


141 


89-867 


46-6 


142 


84-974 


45-5 


143 


80-085 


- 44-5 



These results, when plotted on the temperature-concentration diagram in fig. 9, give 
four continuous curves, the right-hand branch being the naphthalene-solubility curve 
and the three left-hand branches being the solubility curves for the three modifications 
a, /3, and y of the acid. 

It will be seen also that there are three different eutectics for naphthalene and the 
three modifications of the acid ; the eutectic for the a-modification and naphthalene is 
at 53, the composition of the mixture being 30'5 percent, naphthalene, 69'5 per cent. 
monochloracetic acid ; the eutectic for the ^-modification and naphthalene is at 50'4 
when the composition of the mixture is 26'25 per cent, naphthalene, 7375 per cent, 
acid ; and the eutectic for the y-modificatioii and naphthalene is at 44 0- 8 when the 
composition is 18'1 per cent, naphthalene, 81 - 9 per cent. acid. The freezing-point 
curve obtained by CADY agrees very approximately with the naphthalene and 
a-branches here determined, CADY obtaining a eutectic at 53'5 for a mixture of 
composition 2 1 J'4 per cent, naphthalene, 70'6 per cent. acid. 

In all four branches it has been found possible to continue the solubility curves a 
little below the various eutectics, and even below some of the supersolubility curves, 
by cooling the mixture somewhat rapidly in an open tube to below a certain 
temperature and then inoculating with a minute fragment of the required crystal, 
which is then carefully watched as the temperature continues to fall slowly. The 
rapid cooling appears to prevent the spontaneous crystallisation of the other 
component of the mixture which would normally occur at a somewhat higher 
temperature had the cooling been gradual. 

This method was also employed in obtaining similar points on the solubility curves 
below the eutectic for mixtures of salol and betol. 

II. The Supersolubility Curves for Mixtures of Naphthalene and Monochloracetic Acid. 

It has been mentioned in the introduction to this paper that preliminary experiments 
on the spontaneous crystallisation of mixtures of naphthalene and monochloracetic 
acid yielded a definite supersolubility curve on the side of the curve representing 
excess of naphthalene above the eutectic composition, but on the other side of the 



SPONTANEOUS CRYSTALLISATION OF MONOCHLOHACETIC ACID, ETC. 373 



turve, corresponding to mixtures containing excess of monochloracetic acid, spontaneous 
(crystallisation took place at different temperatures. From what has now been 
ascertained with regard to monochloracetic acid it might safely be predicted that 



a Solubility 

ft Solubility 
y Solubil 



curve 
curve 

cur 

rsolubilit 1 




90 



100 



20 30 40 50 60 70 80 

Percentage of Naphthalene in Mixture. 

these different temperatures of spontaneous crystallisation correspond to the various 
modifications of the acid. This prediction has been verified by a long series of 
experiments on the temperatures of spontaneous crystallisation of the various mixtures 



374 PRINCIPAL HENRY A. MIERS AND MISS FLORENCE ISAAC ON THE 

enclosed in sealed glass tubes. Fragments of glass or of corundum were also enclosed 
in the tubes with the various mixtures, and the tubes were heated to about 70 or 80 
uatil the crystals had completely dissolved. They were then shaken violently by 
hand as they cooled in a water-bath, and the temperature at which the dense shower 
of spontaneous crystallisation occurred was noted. Each mixture will crystallise 
either as naphthalene or the a-, ft-, or y-modification of the acid, and will therefore 
give a point on one or other of the four branches of the supersolubility curves. As 
soon as crystallisation took place in a tube, it was immediately examined under the 
microscope, and the crystals which had formed were identified. After an intimate 
acquaintance with the various crystals, it was, however, found quite easy to identify 
them with the naked eye as soon as they formed in the tube, and in some cases this 
was necessary, as the change of temperature caused by taking the tube out of the 
water-bath and examining it under the microscope sometimes caused the second 
component of the mixture to crystallise as well as the original shower to increase, or 
the change of temperature sometimes caused a transformation from one modification 
of the acid to another. 

The nature of the material introduced into the tube to produce friction appears to 
have considerable effect on the temperature of spontaneous crystallisation, and also 
operates in bringing down certain modifications. For instance, corundum enclosed in 
a tube containing a certain mixture will bring down an a- or /J-shower much more 
frequently than a y- or naphthalene shower. Tubes containing glass fragments give 
y- and naphthalene showers more readily than a- or /3-showers, and when an a- or 
/3-shower does occur in a tube containing glass fragments it usually does so at a lower 
temperature than in a tube of equal concentration containing corundum. The glass, 
however, appears to be quite as effectual as corundum in bringing down showers of 
naphthalene or of the y-modification of the acid. As in the aqueous solutions of the 
acid, /3-showers occur much more frequently than a-showers. 

The following is a record of all the results obtained for the spontaneous crystal- 
lisation of liquid mixtures of naphthalene and monochloracetic acid by shaking the 
sealed tubes violently by hand in a cooling water-bath, and the observations are 
plotted in fig. 9. 



SPONTANEOUS CRYSTALLISATION OF MONOCHLORACETIC ACID, ETC. 375 
1. Tubes giving Naphthalene Showers. 



Experi- 
ment. 


Concentration of naphthalene in 
the tube. 


Temperature of spontaneous crystallisation. 




per cent. 





144 


100 with glass fragments 


77 


145 


88-922 


72-7, 72-5, 72-5, 72-3 


146 


80 


70-7, 70-5, 70-2 


147 


69-7 


66-9 


148 


60 ; 


64-2, 64-4, 64-2, 64, 64-4 


149 


50-02 


60-2, 59-9 


150 


40-035 


56-4, 56-4, 56-7, 56-8, 56-8, 56-7 


151 


30-04 


49-2,'50-S, 49-6 


152 


23-27 corundum fragments 


45-8, 45-5 


153 


22-958 


46, 46 


154 


17-5 


43-5, 42-5, 42-5 


155 


14-703 


42-5, 42-5 


156 


10-133 , glass fragments 


40-5, 40-5, 41 



The first six of these tubes were heated in oil to about 90 to dissolve the crystals 
and were cooled in an oil-bath and shaken by hand, as described above. 

2. Tubes giving a.-shotvers. 



Experi- 
ment. 


Concentration of acid in the tube. 


Temperature of spontaneous crystallisation. 




per cent. 


= 


157 


100 with corundum fragments 


52 


158 


90-049 


48 5 


159 


89 867 ,, glass fragments 


44, 44, 46-8 


160 


85-297 corundum fragments 


46-5 


161 


85-06 


46-5, 46-5 


162 


80 "085 glass fragments 


44-5 


163 


80 06 corundum fragments 


46, 45-5 


164 


77-015 


45-8 



3. Tubes giving fi-shoivers. 



Experi- 
ment. 


Concentration of acid in the tube. 


Temperature of spontaneous 


crystallisation. 




per cent. 


o 




165 


100 with corundum fragments 


50 




166 


90-049 


47-2, 47, 47, 47-2, 47 


, 47, 47-2 


167 


85-297 


46, 45-5, 46 




168 


80-06 


43-5, 45-5, 45-5, 45-5, 45, 44-8, 44-5 


169 


78 


44-5, 44-5 




170 


77-015 


45, 45 




171 


76-73 


45, 45 





376 PRINCIPAL HENRY A. MIERS AND MISS FLORENCE ISAAC ON THE 

4. Tubes giving y-showers. 



Experi- 
ment. 



Concentration of acid in the tube. 



Temperature of spontaneous crystallisation. 



172 
173 
174 



per cent. 

100 with glass fragments 

89-867 

85 '06 corundum fragments 



47 

42, 41 
38, 39, 39-5 



Discussion of Results and Conclusion. 

It will be seen that in several experiments a single tube has given a shower of the 
same crystals at several different temperatures, but the highest temperature obtained 
is the real temperature of spontaneous crystallisation, and in the other cases the 
mixture must have passed a little into the labile state for the modification in 
question, either in consequence of insufficient shaking or too rapid cooling. In 
plotting these results, therefore, on the temperature-concentration diagram of fig. 9 
the highest temperature at which any mixture crystallised is taken to be the true 
temperature of spontaneous crystallisation. 

Also, in plotting the supersolubility curve from the results of the experiments 
giving a-showers, experiments 159 and 162 are disregarded, since they contain glass 
fragments instead of corundum, and it was found that in tubes of almost exactly 
the same composition containing corundum fragments (experiments 158 and 163) the 
spontaneous crystallisation occurs at a considerably higher temperature. 

With these limitations experiments 144 to 174 will give the four branches of the 
complete supersolubility curve for mixtures of naphthalene and monochloracetic acid. 
They appear on fig. 9 together with the corresponding solubility curves. They are 
fairly continuous curves, each running approximately parallel to the solubility curve 
with which it corresponds. The two a-curves are separated by an interval of between 
9 and 10 of temperature, the two /3-curves by an interval of about 5, and the two 
y-curves by between 3 and 5, while the two naphthalene curves are separated by 
between 2 and 3. The three branches of the supersolubility curve for monochlor- 
acetic acid meet the naphthalene supersolubility curve in three points, thus giving 
three hypertectic points at their intersections, just as three eutectics are given by 
the solubility curves. These points occur at (i) 46 with composition 23 per cent, 
naphthalene 77 per cent, acid, for naphthalene and the a-modification of the acid ; 
(ii) 45 with composition 121 '5 per cent, naphthalene 78 - 5 per cent, acid, for 
naphthalene and the /3-modification of the acid; and (iii) 41'3 with composition 
11 per cent, naphthalene 89 per cent, acid, for naphthalene and the y-modifi cation of 
the acid. 

It may also be seen that the ft- and y-supersolubility curves even cross the 
naphthalene supersolubility curve a little, thus yielding spontaneous crystallisation 



SPONTANEOUS CRYSTALLISATION OF MONOCHLORACETIC ACID, ETC. 377 

below their hypertectics ; these points were obtained in the usual way during the 
course of the experiments. 

The curves of fig. 9 also show that in a mixture of two substances, one of which 
exists in three modifications, eight freezing-points may be exhibited by a given 
mixture as it cools. For example, the mixture of composition 15 per cent, 
naphthalene 85 per cent, monochloracetic acid has yielded (i) crystals of the 
a-modification of the acid by inoculation with a at 56 0- 5 ; (ii) crystals of the 
/^-modification by inoculation with /8 at 50'5 ; (iii) a labile shower of a-crystals at 
46'5 ; (iv) a labile shower of ^-crystals at 46 ; (v) crystals of the y-modification by 
inoculation with y at 45'5 ; (vi) naphthalene crystals by inoculation at 43 0- 5 ; (vii) a 
labile shower of naphthalene at 42 0- 5 ; and (viii) a labile shower of y-crystals at 39 0- 5. 
Mixtures of other compositions exhibit multiple freezing-points in the same way. 

Further, the four solubility and four supersolubility curves of fig. 9 may be seen 
to divide the whole diagram into twenty different regions, in each of which the 
crystallisation of a mixture of naphthalene and monochloracetic acid may occur in a 
different manner. For example, in the region bounded by DD, EE, GG, and HH, 
, /3, or naphthalene may form by inoculation, or a inay form spontaneously, since in 
this region any mixture is labile with respect to , metastable with respect to ft 
and naphthalene, but unsaturated with respect to y. 

It must be mentioned that in these experiments on mixtures the monochloracetic 
acid used was the commercial acid, and, although it was always dried for several days 
in a desiccator, it almost certainly contains about 1 per cent, of water, so that the 
results are slightly affected by this throughout. 

In conclusion, we may say that, although this research has not yielded information 
concerning the crystallisation of a series of mixed crystals with minimum freezing- 
point as we had at first hoped, it has shown the manner in which the crystallisation 
of the different modifications of a substance occurs, when this substance is dissolved in 
water or in some other substance which is not polymorphous, such as naphthalene ; and 
it has also shown that each modification of a polymorphous substance possesses a 
definite and different temperature of spontaneous crystallisation. This conclusion is 
of some theoretical interest, for it suggests that in the cooling liquid one -modification 
may come into existence after another and be ripe for crystallisation while still in the 
liquid state. 



VOL. CCIX. A. 3 C 



[379] 



XV. On the Electricity of R'lin and its Origin in TJmnderstorms, 

By GEORGE C. SIMPSON, D.Sc. 
Communicated by DR. GILBERT T. WALKER, F.R.S. 

(Received January 6, Read February 11, -Revised April 14, 1909.) 

SINCE FRANKLIN first showed that thunder and lightning are caused by electrical 
discharges, there have been numerous theories to account for the production of 
electricity in thunderstorms, but none has been generally accepted by meteorologists. 
When attacking the problems of thunderstorm electricity, two methods naturally 
present themselves : we may either investigate the actual phenomena in the 
atmosphere, or try to repeat on a small scale in the laboratory the processes which 
may be supposed to take place during thunderstorms. During 1907-8 an 
investigation was undertaken on both these lines at the Meteorological Office of the 
Government of India in Simla. A systematic record was obtained by automatic 
instruments of the electricity brought down by the rain during practically the whole 
of one rainy season, and laboratory experiments were made to find the origin of the 
electricity of thunderstorms. The work has resulted in the formation of a new 
theory, which appears to account in a satisfactory manner for the electrical effects 
observed during thunderstorms. 

The following paper is divided into three parts : Part I deals with the 
measurements of the electricity of the rain, Part II with the laboratory experiments, 
and Part III contains the new theory based on the results detailed in the previous 
parts. 

PART I. Measurements of the Electricity of the Rain. 

The electricity brought down by rain had previously been measured by ELSTER 
and GEITEL* in Wolfenbiittel, by GERDiENf in Gottingen, and WEISSJ in Vienna. 
The apparatus used in Simla differed from the form used by each of these in several 
particulars, chiefly in that it was entirely self-registering and was kept constantly 
in action during the whole of the rainy season, whether precipitation was expected 
or not. 

The final form of the Simla apparatus is diagrammatically shown in fig. 1. 
A corrugated iron hut, 8 feet square, was erected on a suitable site in the grounds 

* ELSTEK and GEITEL, 'Wien. Ber.,' vol. 99, Abth. II. a, p. 421, 1890; 'Terr. Magn.,' vol. 4, p. 15, 
1899. 

t GERDIEN, 'Phys. Zeit.,' vol. 4, p. 837, 1903. 
t WEISS, 'Wien. Ber.,' vol. 115, Abth. II. a, p. 1285, 1906. 
VOL. CCIX. A 455. 3 C 2 12.8.09. 



380 



DR. G. C. SIMPSON ON THE ELECTEICITY OF 



of the residence of the author. Through a hole in the centre of the roof the rain fell 
into an insulated receiver AA which was connected to a self-registering electrometer. 




FIG. 1. 



In order to prevent the rain which fell on to the roof near the hole from splashing 
into the receiver, a galvanised iron cylinder BB was fitted to the hole with its top 



RAIN AND ITS ORIGIN IN THUNDERSTORMS. 381 

20 cm. above the level of the roof and its lower end just within the hut. To prevent 
the rain-water which struck the sides of this cylinder from running into the 
receiver, a conical rim CO was soldered inside the bottom of the cylinder and the 
water was drained away through the pipe D. This rim reduced the effective opening 
through which the rain fell to a diameter of 29 cm. 

The receiver AA, which was placed immediately below the bottom of the cylinder, 
was a galvanised iron vessel 50 '5 cm. in diameter and 31 cm. deep, having a 
slightly rounded bottom so that the water which fell into it ran off through the pipe 
EE. The receiver was supported on three legs, which passed freely through three 
holes in the top of the case FF, each being insulated on a sulphur-coated ebonite 
rod I fitting into a firm tripod fixed on to the bottom of the case. 

The potential of the receiver was recorded automatically every two minutes by 
means of a Benndorf* self-registering electrometer G of the usual pattern, registering 
in the following way : To the needle of a quadrant electrometer a long aluminium 
boom is attached and swings freely over a strip of paper 12 cm. wide, which is slowly 
moved forwards by means of a clock. Every two minutes the clock closes an electric 
circuit which actuates a magnet and causes a bar to press the end of the boom 
sharply into contact with the paper through a typewriter ink ribbon. In this way 
the paper receives a series of dots each representing the position of the boom, i.e. 
the deflection of the needle, at the instant the circuit was closed. In order to mark 
the time a second circuit is closed each hour, and a magnetic is thus excited which 
causes two dots to be imprinted, one on each side of the paper exactly in a line with 
the end of the boom ; thus the line joining these dots is at right angles to the 
length of the paper, and would pass through a dot made at the same time by the 
boom. This device will be referred to later as the " hour marker." As shown in the 
figure, the Benndorf electrometer was placed within the case FF. 

When the receiver was connected to the Benndorf electrometer and it received no 
charge, a series of dots was printed on the paper in a straight line, but when a 
charge was imparted to the receiver the needle of the electrometer was deflected and 
with it the boom, so that the dot made at the end of the next two minutes' interval 
indicated the amount of the deflection. If the instrument were then left to itself 
and received no further charge, the record would show a series of dots in a curved 
line inclined to the zero line. The inclination of this line was a measure of the rate 
of leak from the charged system. 

For the purposes of measuring the charge brought down by the rain, an earthing 
device H was brought into use. This consisted of a light earth -connected wire 
which, by means of an electromagnet, could be brought into contact with the 
receiver and connect it to earth. This magnet was excited by the current which 
caused the registration of the electrometer, so that at the instant that the potential 
of .the receiver was registered the latter was also connected to earth. In this way 

* BENNDORF, 'Phys. Zeit.,' vol. 7, p. 98, 1906. 



382 DR. G. C. SIMPSON ON THE ELECTRICITY OF 

each dot on the paper indicated the charge which the receiver had obtained from 
the rain in two minutes. This earthing magnet could be disconnected when it was 
desired to test the insulation of the system by the method described above. 

The amount of rainfall was recorded in the following way : The end of the metal 
pipe EE which drained the water from the receiver ended within a vertical cylinder 
J. From the end of the pipe the water fell in large drops, and since the drops 
detached themselves from the pipe well within the cylinder they carried away no 
electricity. The drops then fell into the funnel of the rain-gauge K. This was of 
the ordinary tipping bucket pattern, recording on a drum which revolved in 24 hours. 
One slight alteration was however made. Instead of allowing the pen to be always 
touching the paper, it was only brought into "contact with it for a moment at the 
end of each two minutes' interval, this being effected by means of an electromagnet 
actuated by the current, which excited every two minutes the magnets already 
referred to. As every dot on the rain-gauge trace corresponded with a dot on the 
electricity trace, it was possible to correlate the two records and find how much rain 
corresponded with each deflection of the electrometer. In order to make this 
correlation quite certain the electrical circuit which actuated the " hour marker " of 
the Benndorf electrometer was disconnected from the clock and arranged so that the 
circuit was automatically closed for an instant each time the bucket tipped. Thus 
every time the bucket tipped a dot was printed on each side of the electrometer 
trace, and if the rain was only light, so that the bucket tipped only once in about 
two minutes, the number of tips could be counted from the dots. If, however, the 
rainfall was rapid these dots were not separated but formed a line ; the rainfall was 
then measured for eacli two minutes' interval from the rain-gauge trace. 

This method of measuring the rainfall had one serious drawback. The rain was 
only registered when the bucket tipped, and as this only took place when 0'014 cm. 
of rain had fallen, the registration was not satisfactory with light rain. The 
registration was also not satisfactory at the beginning of a shower, for in this case 
the first tip did not t;ike place until after considerably more than 0'014 cm. of rain 
had fallen, owing to a certain amount of water being used up in wetting the receiver 
and the pipe through which the water passed from receiver to gauge. Nevertheless, 
after the first tip and when the rain was not very light the method worked 
admirably and gave practically no trouble in use. In fig. 1, for the sake of clearness, 
the rain-gauge is shown out of place. In use it was behind the case FF, in which 
position the tube EE was much shorter than it has been necessary to show it in the 
diagram. 

The corrugated walls of the hut were carried, as shown in the figure, to. a height 
of about two metres above the roof of the hut. This was done in order to protect 
entirely the mouth of the receiving apparatus from the earth's electrical field, and 
to prevent the wind from sweeping across the mouth of the cylinder CC, which 
would have interfered with the entrance of the rain into the receiver. 



BAIN AND ITS OKIGIN IN THUNDERSTORMS. 383 

During the course of the experiments two additions were made to the apparatus 
just described, which it had not been possible to get ready before the first few storms 
occurred. 

A second Benndorf electrometer L was added to record the potential gradient. 
It is almost impossible to get a satisfactory method of recording the potential 
gradient during thunderstorms, because the changes in the gradient take place 
more rapidly than the instruments used can follow them, and the range over which 
the potential gradient varies is extreme. It was therefore considered sufficient to 
record only the predominant sign of the potential gradient during each two minutes' 
interval. This was done by putting an insulated bamboo rod MM, having an 
umbrella rib attached to its end, through a window into the open air, and connecting 
it to the second Benndorf electrometer.* It was also arranged that this simple 
collector should be connected to earth at the end of each two minutes. The same 
current which recorded on the first Benndorf electrometer was used for the second, 
and the records were thus simultaneously taken. 

The second addition consisted of an arrangement to record the lightning 
discharges. A long wire was carried from the open air into the hut and connected to 
a coherer fitted with the usual decohering device. The current of the latter passed 
through the circuit of the " time marker " on the second Benndorf electrometer, 
so that each lightning discharge was recorded by dots on the edges of the paper 
which was receiving the record of the potential gradient. The coherer was 
purposely made somewhat insensitive in order not to record distant discharges, 
and on this account it often missed weak near discharges. The device, therefore, 
could not be said to count the number of discharges, but it gave a good idea as to 
whether the rainstorms were accompanied by many or few electrical discharges. 

During the monsoon, for weeks together, the humidity of the air practically 
remained at 100 per cent., and thus everything, both indoors and outdoors, became 
very damp. Under such conditions, provision had to be made for keeping the 
insulation of the instruments in good condition. This was done by arranging that 
all insulators should be within the case FF, which was kept warm by continuously 
burning a lamp under the lower end of a pipe, 7 cm. in diameter, passing through 
the case in the manner shown in fig. 1. This precaution prevented all difficulty 
with the insulation of the instruments ; but another difficulty connected with 
insulation could not be entirely avoided. This was caused by spiders spinning their 
webs from the insulated parts of the system to earth-connected objects. Since the 
collector of the potential gradient apparatus had to be exposed in the open air, it 

* The rod carried a small tube containing radium at its end, but it is not believed that this materially 
assisted the equalisation of potential between the rod and the surrounding air, the ordinary " dissipation " 
at the end of the rod being sufficient for the purpose. The capacity of the rod being small, the quantity 
of electricity accumulated at the end of the rod did not in the author's opinion disturb sensibly the 
lines of force in the neighbourhood of the rod. [April 14, 1909.] 



384 DE. G. C. SIMPSON ON THE ELECTKICITY OF 

was very often subjected to this trouble, and many records of the potential gradient 
were lost in consequence. The only means which could be devised to diminish the 
difficulty was to take every opportunity of visiting the instruments and sweeping 
away the webs. 

After the instruments had been set up, the question had to be decided how 
sensitive to make the electrometer. In view of the fact that the work was being 
undertaken mainly with a view to the investigation of thunderstorms, it seemed 
desirable that the sensitiveness should be so arranged that the deflection should 
never be greater in two minutes than would bring the boom of the electrometer to 
the edge of the paper on which the record was being made. This necessitated a 
somewhat low sensitiveness, and, as a consequence, the electricity of rain with very 
low charges could not be measured. There was the possibility of altering the 
sensitiveness of the instrument according to the kind of rain which was expected, 
but this was considered impracticable in view of the fact that the instrument could 
not be watched continually, but had to be left to itself to take the records entirely 
automatically. In reality, this difficulty was not serious. The conditions during 
thunderstorms are entirely different from those during gentle rain, and to investigate 
the two cases is really a matter of two distinct researches. The present research 
was concerned with highly charged rain, and so the fact that the instrument did not 
also record very small charges was not of any great consequence. 

By good fortune, after the first one or two storms, a degree of sensitiveness was 
found which proved to be satisfactory during the rest of the rains. On only two 
or three occasions did the boom pass to the edge of the paper, and on each of these 
occasions the instrument was under observation, so that a rough estimate could be 
made as to what would have been the extent of the deflection from the time taken 
for the boom to reach the stop. This sensitiveness gave a deflection of 1 cm. for 
40 volts, and, as a deflection of 0'2 mm. could be recognised with certainty, a 
potential of 1 volt could be measured. The capacity of the receiving system was 
determined to be 141 cm., and hence the smallest charge which could be measured 
with certainty was 0'47 electrostatic unit. The rain entered the receiver through 
an opening 29 cm. in diameter, so that when a charge of 7 X 10~ 4 electrostatic unit 
fell on each square centimetre of surface in two minutes it was sufficient to be 
recorded by the instrument. 

In order to determine the charge brought down by each cubic centimetre of rain 
it was only necessary to divide the charge registered by the electrometer during any 
two minutes by the amount of rain recorded by the rain-gauge during the same 
interval of time. On account, however, of the limitation of the method of recording 
the rainfall already pointed out, it was not possible to find the value of the charge 
per cubic centimetre of rain from electrometer and rain-gauge records for every 
single two minutes' interval ; but experience showed that it was exceptional not to 
be able to do so, and during the greater part of the rains this value was obtained. 



RAIN AND ITS OEIGIN IN THUNDERSTORMS. 385 

The degree of accuracy to which this measurement could be made during heavy rain 
or highly charged light rain was 01 electrostatic unit per cubic centimetre of 
rain-water. A charge of O'l electrostatic unit of electricity on a cubic centimetre of 
rain was taken as the lowest charge with which the research was concerned. All 
charges less than this amount were written as nil. 

Before discussing the results of the electrical measurements, it is desirable to give 
a short description of the character of the rain in Simla during the period when the 
measurements were made. The months of April and May are the hot months of the 
year. But although Simla is at an elevation of about 7000 feet above sea level, 
and the temperature does not therefore rise very high, yet the almost uninterrupted 
sunshine during these two mouths is very favourable to the formation of thunder- 
storms. In 1908, the first thunderstorm occurred on April 5, and afterwards storms 
of greater or less intensity occurred at intervals of seldom longer than a fortnight. 
The monsoon normally arrives in the Simla hills during the second half of June, and 
previous to its arrival the thunderstorms become more and more frequent, culminating * 
in storms of some violence which accompany the actual arrival. In the year under 
review it was difficult to fix a definite day for the setting in of the monsoon, because 
of the gradual manner in which the changes occurred. 

The greatest storm of the year occurred 011 July 1, and afterwards the thunder- 
storms became less frequent and the monsoon rainfall more steady and continuous. 
From this date the monsoon gave more or less heavy rain each day and continued 
until the beginning of September ; as usual it ended with one or two sharp 
th understorms. 

From the beginning of the thunderstorms in April to the end of the rains in 
September the part of the apparatus for measuring the rainfall and the electricity 
associated with it was in constant action, so that the electrical state of nearly every 
shower was recorded. The potential gradient and coherer records commenced on 
June 18 and the latter were entirely free from failure. The data used in the 
following discussion have been obtained from every storm during which any 
electricity was recorded, however light the rain, and also from those storms during 
which no electricity was measured, but rain fell at a greater rate than 0'007 cm. in 
each two minutes' interval. The latter limitation has been chosen because with 
a rainfall of this amount charged to O'l els. unit per cubic centimetre of rain the 
electrometer would have shown the smallest measurable deflection. Thus when the 
rainfall was heavier than this amount and no electricity was recorded it could be said 
with certainty that the rain was not charged to O'l els. unit per centimetre, while 
with lighter rainfall which showed no electricity the same conclusion could not be 
drawn ; it was therefore considered best to neglect such lighter rainfall. 

It has been found impracticable to divide the storms observed into thunderstorms 
and storms which were not thunderstorms. For three months rain fell nearly every 
day and it was quite impossible to take notes during the whole time that the rain 

VOL. ccix. A. 3 D 



386 DR. G. C. SIMPSON ON THE ELECTRICITY OF 

was falling in view of the routine work of the department. Nor do the coherer 
records allow of such a division being made, for the coherer often recorded one or two 
discharges on days when no thunder was heard and little rain fell. Thus the 
difference between rain of this latter type which could not be called thunder rain and 
that associated with much thunder and lightning was simply a matter of degree and 
not of kind. For this reason the rainstorms have in the following analysis generally 
been treated irrespectively of whether the rain was accompanied by electrical 
discharges or not. 

Want of space makes it impossible to give here the detailed results of the 
measurements. The figures are, however, to be published in extenso in part 8, 
vol. 20, of the ' India Meteorological Memoirs.' 

Results. 

The aggregate amount of rain which fell during the periods of rainfall investigated 
. was 76 '3 cm. 

The electrometer trace registered charged rain during 1926 two minutes' intervals, 
during 13G2 of which the electrometer recorded positive electricity, and during 
564 negative electricity. The total quantity of positive electricity which fell on each 
square centimetre of surface was 22 '3 electrostatic units and of negative electricity 
7 '6 units. 

From this it is seen that 2 - 9 times as much positive as negative electricity fell 
during the rains and that the time during which positive rain fell was 2'4 times 
longer than that during which negative electricity fell. This result is of great 
importance in view of the generally accepted belief that much more negative than 
positive electricity is brought down by the rain, a belief on which several theories of 
atmospheric electricity have been based. 

When charged rain is falling the effect is equivalent to a vertical current of 
electricity ; with positively charged rain the current may be considered to be flowing 
from the atmosphere into the ground, and with negatively charged rain from the 
ground into the atmosphere. The values of the currents attained in this way are of 
considerable importance from the points of view of both atmospheric electricity and 
of terrestrial magnetism. 

An analysis of the data for this purpose is given in Table I. 

In this table, column 2 contains the number of times positive currents (i.e. currents 
caused by positively charged rain) were recorded with values between the limits 
shown in the first column, and similar data for negative currents are given in 
column 3. 

Neglecting for a short time currents greater than 300 X 10~ 15 ampere we see that 
large currents are more seldom met with than smaller currents, this being true for 
both positive and negative currents. The most important fact, however, is that as 
the currents become larger the frequency with which positive currents occur tends 



RAIN AND ITS ORIGIN IN THUNDERSTORMS. 
TABLE I. 



387 





No. of two minutes' intervals during 




Current in 10~ 15 amp. 


which the current was 


No. of positive intervals. 


per sq. cm. 




No. of negative intervals. 








Positive. 


Negative. 




2- 50 


1058 


511 


2-1 


50-100 


165 


48 


3-4 


100-150 


81 


17 


5-0 


150-200 


33 


5 


6-6. 


200-300 


31 


4 


8-0 


>300 


15 


18 






to become much greater than the frequency with which negative currents occur. In 
other words, the greater the current the more likely is it to he carried by positively 
charged rain. 

To these deductions the data for currents greater than 300 X 10~ 15 ampere appear 
to be exceptions. But as 15 of the 18 negative currents greater than 
300 X 10~ 15 ampere were recorded in a single and very abnormal storm on 
May 13, the relation shown must be considered accidental. The values of the 
greatest currents are of particular interest and the following list is therefore given of 
all those having a greater value than 300 X 10~ 15 ampere. 

TABLE II. 



Positive currents. 


Negative currents. 


Amps, x 1Q- 15 . 


Date. 


Amps, x 10~ 15 . 


Date. 


419 


April 7 


345 


Miy 13 


416 


May 9 


356 


13 


830* 


, 9 


400 


13 


830* 


, 9 


410 


13 


406 


, 9 


392 


13 


400 


, 13 


392 


13 


990* 


Juy 19 


341 


13 


990* 


19 


341 


13 


990* 


19 


436 


13 


690* 


19 


392 


13 


327 


19 


366 


13 


436 


19 


362 


13 


352 


August 18 


396 


13 


386 


September 13 


352 


13 


396 


13 


392 


13 






331 


July 29 






428 


99 

,, -ij 






331 


')Q 
-.J 



* These values are estimated from the time it took the boom to reach the stop at the edge of the paper 
and are therefore only approximate. 

3 D 2 



388 



DK. G. C. SIMPSON ON THE ELECTRICITY OF 



A current of a given value may be made up in two ways : (1) by light rain 
carrying heavy charges ; or (2) by heavy rain carrying light charges. Hence it will 
be interesting to investigate the charges brought down by a given quantity of water 
and then to see how these charges vary with the rate of rainfall. 

TABLE III. 





No. of two minutes' intervals during 




Charge per c.c. of 


which the charge was 


No. of positive intervals. 


rain, els. units. 




No. of negative intervals. 








Positive. 


Negative. 




<0-1 


911 




0-1-1 


837 


305 


2-7 


12 


148 


56 


2-6 


2-3 


52 


25 


2-1 


3-4 


3<n 


6^| 




4-5 


9 I 


8 lo- 




5-6 


9 [ 71 


af 37 


1-9 


>6 


14J 


20j 





Table III shows the number of two minutes' intervals during which rain having 
different charges was recorded. It will be seen that although these numbers do not 
indicate any marked change in the proportion of positively charged rain as the 

TABLE IV. 



Positive charge per c.c. of rain. 


Negative charge per c.c. of rain. 


Els. units. 


Date. 


Els. units. 


Date. 


+ 7-2 


April 7 


-6-6 


April 12 


6-3 


7 


6-6 


12 


6-1 


8 


6-5 


May 13 


6-0 


13 


6-5 


13 


6-0 


13 


17-7 


13 


6-0 


26 


17-7 


13 


6-0 


26 


10-1 


13 


6-0 


May 13 


10-4 


, 13 


6-2 


13 


6-4 


13 


6-2 


13 


19-8 


, 13 


8-0 


13 


19-8 


, 13 


8-0 


13 


8-6 


, 13 


7-7 


June 9 


15-2 


, 13 


7-7 


9 


15-2 


, 13 






11-0 


, 13 






9-3 


, 13 






9-1 


, 13 






8-9 


, 13 






12-0 


, 13 






12-0 


, 13 



RAIN AND ITS ORIGIN IN THUNDERSTORMS. 



389 



charges become greater, they do indicate a slight tendency for the ratio of positive to 
negative electricity to become less as the charges increase ; but it would not be safe 
to base any deductions on the slight variations indicated. 

The effects of the storm of May 13 are again seen in the figures for highly 
charged negative rain ; for of the 20 records of rain with higher negative charges 
than 6 els. units per cubic centimetre of water, 18 occurred during this one 
storm. 

Table IV is a list of the charges which equalled or exceeded 6 els. units per 
cubic centimetre of water. 

From this it will be seen that during the storm on May 13 the negative 
charge on the rain reached the large amount of nearly 20 els. units per cubic centi- 
metre of water. With the exception of these the largest charges were positive 
charges of 8 els. units per cubic centimetre of water. 

We can now turn to the question whether there is any relationship between the 
rate of the rainfall and the charge it carries : 

TABLE V. 



Rate of 
rainfall, mm. 


Rain with 
no charge. 


Rain with positive 
charge. 


Rain with negative 
charge. 


Ratio of number 
of positive to 
number of 












of rain in 
two minutes. 


No. of two 
minutes' 
intervals. 


No. of two 
minutes' 
intervals. 


Mean charge 
per c.c. of 
rain in 
els. units. 


No. of two 
minutes' 
intervals. 


Mean charge 
per c.c. of 
rain in 
els. units. 


negative 
two minutes' 
intervals. 


<0-14 




187 


1-7 


168 


2-2 


1-1 


0-14 


441 


277 


1-0 


152 


1-0 


1-8 


0-28 


153 


223 


0-6 


68 


0-5 


3-3 


0-42 


53 


91 


0-4 


20 


0-5 


4-5 


0-56 


22 


70 


0-2 


15 


0-4 


4-7 


0-70 


6 


54 


0-3 


10 


0-6 


5-4 


0-84 


2 


45 


0-2 


7 


o-o 


6-4 


0-98 





23 


0-3 


4 


o-o 


5-8 


1-12 





24 


0-4 









1-26 





14 


0-4 









1-40 





14 


0-3 









1-54 





10 


0-3 









1-68 





7 


0-5 









1-82 


0' 


4 


0-3 









1-96 





3 


0-1 









2-10 





5 ' 


0-2 









2-24 





3 


0-4 









>2-24 





13 


0-3 










In this table, columns 2, 3, and 5 give the number of two minutes' intervals 
during which rain, having the intensities shown in the first column, was recorded as 
bringing down no charge, a positive charge, and a negative charge respectively ; while 



390 DE. G. C. SIMPSON ON THE ELECTEICITY OF 

in columns 4 and 6 the corresponding mean charges per cubic centimetre are tabulated. 
Column 7 gives the ratio of the number of two minutes of positive rain to the number 
of two minutes of negative rain. 

Two interesting results are shown in this table, the most important being that the 
ratio of the number of positively charged falls to negatively charged falls increases as 
the rainfall becomes more intense. In this respect it is important to notice that in 
no case in which the rainfall exceeded 1 mm. in two minutes was a negative 
charge associated with the rain. The second interesting result is that both with 
positively and negatively charged rain the highest charges are carried down by light 
rain, although with heavier rain than 0'028 cm. in two minutes the magnitude of the 
charge does not appear to depend on the intensity of the rain. 

The general character of the rain in reference to its electrical state may now 
be discussed, starting with the rain which accompanied thunderstorms. 

It has already been pointed out that a hard and fast line cannot be drawn between 
rain which falls (luring thunderstorms and rain not connected with thunderstorms. Still 
there can be no possible doubt that the rain connected with thunderstorms was more 
highly charged than rain with which were associated few lightning discharges or none 
at all. During some storms in July and August, which were not accompanied 
by electrical effects, rainfall exceeding 0'070 cm. in two minutes occurred without giving 
the slightest indication of any electrical charge, while on the other hand it sometimes 
happened that during thunderstorms the rain was too light to be registered on 
the rain-gauge, and yet charged up the receiver to a potential between 20 and 
30 volts in two minutes. It is, however, important to point out that the most highly 
charged rain did not always accompany the storms with the greatest amount of 
thunder and lightning. Also, often during a thunderstorm the rain would continue 
after the thunder and lightning had ceased, and yet be as highly, if not more highly 
charged than during the violent electrical display. 

As a preliminary to discussing the general characteristics of negatively charged 
rain, the remarkable storm of May 13, 1908, which has already been referred to, will 
be considered. 

At about midday the weather appeared threatening and a violent thunderstorm 
worked up soon after 13 hours. The thunder was very loud and near, and the 
lightning vivid. At 13 hours 46 minutes the rain began to fall, but not very heavily. 
The heaviest rain occurred at about 14 hours 36 minutes, the average rainfall being 
then at the rate of 0'042 cm. in two minutes, and the greatest rate 0'070 cm. in the 
same time. At 14 hours 48 minutes the rate of rainfall became less, and from then 
until 17 hours 30 minutes steady rain continued at an almost constant rate of 
0-014 cm. in two minutes. Unfortunately, during the storm it was impossible to 
follow the changes very closely owing to the demands of other work, and hence it is 
not known exactly at what time the thunder and lightning ceased ; there are reasons, 
however, for believing that it did not continue long after 15 hours, and it is known 



RAIN AND ITS OEIGIN IN THUNDERSTORMS. 



391 



for certain that it had ceased before 16 hours.* During the period at the commence- 
ment of the storm, when the rain was moderately heavy and the electrical discharges 
violent, the rain was positively charged, but from 15 hours 24 minutes to 17 hours 
8 minutes, that is, during the steady rain without thunder and lightning, the rain 
carried down a negative charge which at times exceeded 19 els. units per centimetre 
of water, this being by far the greatest charge measured on any rain. This charge is 
so great that the electrical force on the raindrops within a field of half the intensity 
necessary to cause a lightning discharge would be equal to the force exerted by 
gravity on the raindrops, so that it would be quite possible for fields to occur which 
would actually cause such drops to rise against gravity. 

The noteworthy features of this highly negatively charged rain were that it occurred 
after a violent thunderstorm, during which the rain had been positively charged, and 
that the rate at which it fell was not great, but uniform and steady. These 
characteristics of negatively charged rain which were so marked in this storm are 
more or less traceable throughout all the storms investigated. 

It has already been pointed out that negatively charged rain does not occur when 
the rate of the rainfall becomes large, and from Table V, p. 389, it will be seen that 
the rainfall was less than 0'028 cm. in two minutes during 88 per cent, of the time 
that negatively charged rain fell, while for positively charged rain this proportion was 
only 64 per cent. Thus it would appear that negative electricity is, as a rule, brought 
down by light rain. 

Negatively charged rain fell during all periods of the storms, and in some very rare 
cases the whole rain was negatively charged ; but there appeared, from the data 
collected, to be a tendency for negative 'electricity to be associated with the latter 
half of a storm. In order to bring out the relationship, as many storms as possible 
have been divided into four equal parts as regards time, and the occurrences of 
positively and negatively charged rain in each quarter have been counted, with the 
following result : 

TABLE VI. 



Quarter of the storm. 



1st 
2nd 
3rd 
4th 



Percentage of time of rainfall during which 
the charge measured was negative. 



From this it is seen that although more positive than negative rain fell in all periods 
of the storms, the difference was least in the second half, or, in other words, the 



* This storm occurred before the coherer had been installed. 



392 



DK. G. C. SIMPSON ON THE ELECTEICITY OF 



tendency was for negative electricity to be brought down by the rain more generally 
in the second than in the first half of the storms. 

Other characteristics of negatively charged rain were noted in the course of the 
work, namely, that such rain nearly always fell from a lightly clouded sky, and fell at a 
very uniform rate, without the rapid changes in the rate of falling which accompanied 
the positively charged rain. 

The chief characteristics of positively charged rain were that it was always 
associated with the heavy rainfall which accompanied the centre of a thunderstorm, 
and with nearly every case in which the rainfall suddenly increased in violence. Both 
light and heavy rain were more often charged positively than negatively, and on the 
average light rain was more highly charged than heavy rain. 

The relationship between potential gradient and rain electricity will now be 
considered. The potential gradient record did not commence until July 18, and 
owing to spiders spinning their webs from the collector to the surrounding objects 
a good many days' records were lost. In spite of these facts many data were 
collected, and can be used to show the relationship between the signs of the electricity 
of the rain and the potential gradient. Defining the sign of the fine weather potential 
gradient as positive, it may be taken as a general rule that negative potential gradient 
only occurs during periods of disturbed weather. It is a well-known fact that during 
thunderstorms the potential gradient undergoes violent and rapid changes, and these 
changes must in some way be associated with the same electrical effect that causes the 
thunder and lightning. Thus one might expect that a close relationship would exist 
between the sign of the potential gradient and the sign of the rain electricity, but this 
consideration was not borne out by the measurements. 

From the records of the three instruments, potential gradient electrometer, rain 
electricity electrometer, and rain-gauge, it has been possible to pick out 1950 two 
minutes' intervals during which rain fell and the potential gradient was measured. 
From these data the following table lias been constructed : 

TABLE VII. 





No. of two minutes' intervals during 
which the potential was 


Percentage occur- 
rence of negative 
potential gradient. 


Positive. 


Negative. 


Rain uncharged 


245 
267 
117 


668 
437 
216 


72 
62 
65 


Rain charged positively 


Rain charged negatively .... 



From this it will be seen : 

(1) That during rain, whether charged or uncharged, the potential gradient was 
more often negative than positive. 



RAIN AND ITS ORIGIN IN THUNDERSTORMS. 393 

(2) That there was no relationship between the sign of the potential gradient and 
the sign of the rain electricity. 

(3) That the excess of negative potential gradient over positive potential gradient 
was somewhat less when the rain was charged than when it was uncharged, the 
percentages of negative potential gradient in the two cases being 63 and 72 
respectively. 

Before summing up the results of this work, it is desirable to point out the sources 
of error which might be held to influence the results : 

(1) A certain number of raindrops are bound to fall on the rim at the top of the 
cylinder B (see fig. 1, p. 380), and part at least of each drop will probably splash into 
the receiver A. If, now, this rim has high charges induced on it by the influence of 
the earth's field, the drops which break on it will take away some of the induced 
charge and give it up to the receiver when they fall into it. 

This difficulty was guarded against by carrying up the walls of the shed to a height 
of about 1'5 metres above the level of the top of the cylinder B, thus reducing the 
earth's field in the neighbourhood of B as much as possible. But the best proof that 
the results were not affected by this source of error is to' be found in Table VII, which 
shows that the sign of the rain electricity was independent of the sign of the potential 
gradient, which it would not have been if the water which entered the receiver had 
obtained its main charge from the rim. 

(2) The possibility of the " Lenard effect " being a source of error has also to be 
considered. LENARD showed that when a drop of pure water falls on a surface and 
splashes, a separation of electricity takes place, the water retains a positive charge, 
and the air takes a negative charge. If steps are taken to remove the charged air 
from the water by a blast of air, the positive charge on the water can be measured ; 
but if the splashing takes place at the bottom of a fairly deep vessel, not artificially 
ventilated, there is no appreciable separation of electricity. It was for this reason 
that the receiver A was made 3 1 cm. deep. With such a vessel the Lenard effect 
could not play any appreciable part. 

But, again, the results themselves are the best test, for they show positive charges 
which could not be given to water by a single splashing under the most favourable 
conditions in a laboratory. LENARD* found that when a stream of water, in small 
drops of 2 mm. diameter, impinged on a metal plate with a velocity of 18 metres a 
second, and great care was taken to obtain complete separation of the electricity by 
artificial ventilation, each drop developed '2 X 10~ 13 coulomb of electricity. From 
this we find that a cubic centimetre of water developed 0'15 els. unit of electricity. 
It therefore appears unlikely that with raindrops falling on to the bottom of the 
receiver A, and without any ventilation to separate the electricity, anything like such 
a large charge as O'l els. unit per cubic centimetre of water could be given to the 
rain by the Lenard effect. Now a charge of O'l els. unit per cubic centimetre of 

* Loc. cit., p. 626. 

VOL. OCIX. A. 3 E 



394 DR. G. C. SIMPSON ON THE ELECTRICITY OP 

water has been taken as the limit of the accuracy of the electrical measurements in 
this work, hence it may be concluded that the results are not materially affected by 
the Lenard effect. 

The more important results of this work may now be summed up as follows : 

(1) During 71 per cent, of the time that charged rain fell the charge was positive. 

(2) 75 per cent, of the electricity brought down by the rain was positive. 

(3) Light rain was more highly charged than heavy rain. 

(4) All rainfall which occurred at a greater rate than a millimetre in two minutes 
was positively charged. 

(5) The proportion of negative electricity brought down by the rain was slightly 
greater in the second than in the first half of the storms. 

(6) The potential gradient was more often negative than positive during rain. 

(7) No relationship between the sign of the potential gradient and the sign of the 
electricity of the rain could be detected. 

PART II. Laboratory Experiments. 

While the measurements of the rain electricity described in the previous part of 
this paper were being made, a second investigation was undertaken in the laboratory 
of the Simla Meteorological Office, with the object of finding the physical process by 
which electrical separation takes place during thunderstorms. The scheme of the 
research was to imitate as far as possible in the laboratory each process which takes 
place in a thunderstorm and to note any electrical effects. 

A large number of experiments was made with vortex rings composed of air in 
different physical states to see if any electrical separation accompanies the friction 
and mixing of masses of air having different temperatures and humidities ; the 
freezing and thawing of water were examined and a number of other experiments 
made, but all with negative results. A series of experiments was then undertaken 
which was based on the following considerations. 

LENARD* has shown that if air ascends with a greater velocity than 8 metres a 
second no water can fall through the current, for if the drops are below a certain size 
they are carried upwards with the air, while if they are above that size they are 
unstable and quickly break up into smaller drops, which are then carried upwards. 
Now, as will be seen later, it is exceedingly probable that during thunderstorms 
ascending currents much greater than 8 metres a second come into play, and these 
must therefore hold a considerable quantity of water in suspension. This water will 
be constantly going through the process of growing from small drops to large drops, 
only to be broken up into small drops again. If, therefore, the breaking of large 
drops into small drops is accompanied by a separation of electricity, thunderstorm 
electricity might owe its origin to such an effect. 

* LENARD, 'Met. Zeit.,' vol. 39, p. 249, 1904. 



KAIN AND ITS ORIGIN IN THUNDERSTORMS. 395 

In 1892 Professor LENARD* published his well-known work on the electrification 
of water by splashing, and in that work he had made experiments on the question 
here raised, but had come to the following conclusion, which he printed in italics : 
" Thus mere breaking up of the water is just as ineffective as the falling of streams 
of water through the air ; it was only the impact of separate drops upon a flat 
obstacle which produced an electrical effect, "t 

The experiments on which this conclusion was based did not appear conclusive, 
and it was considered necessary to make further experiments before accepting it as 
final. 

The first experiments made led to negative results, but it was soon found that 
this was probably due to the impurity of the water drawn from the Simla mains, for 
even the Lenard effect could not be obtained with it. The experiments were then 
repeated with distilled water, and it was at once found that the mere breaking up 
of large drops into spray on an air jet gave to the water a considerable positive 
charge. 

There is no need to describe in detail the experiments by which this result was 
first obtained, for better methods, capable of giving quantitative results, were 
developed later, and a description of the final experiments will at once be given. 

A metal tray T (see fig. 2), 30 cm. square and 15 cm. deep, was supported on three 
amber insulators I, while through the bottom of the tray, exactly in the middle, 
a vertical piece of glass tube was passed which was drawn out to a nozzle 2 nun. in 
diameter at its upper end. Underneath the tray this glass tube was connected by 
means of a short piece of rubber tube to another glass tube S, which had been coated 
inside and out with sulphur. The latter formed a very highly insulating txibe, by 
means of which the nozzle in the tray could be connected to the air reservoir R and 
air passed through it without any fear of the charge collected on the tray being 
conducted away. The reservoir was supplied with air by means of the foot bellows 
B, and the pressure inside could be kept fairly constant by observing the water 
manometer M. 

At a distance of about 70 cm. above the nozzle a glass funnel F was fixed, 
connected to a glass tube ending within a metal cylinder C. The glass tube was 
filled with wires by which the flow of water out of the funnel could be regulated 
until large drops fell from the end of the tube at the rate of about 80 a minute. 
The cylinder C was insulated from the funnel, and could be either connected to earth 
or to batteries, according as to whether it was desired to have the falling drops 
electrically neutral or charged. 

By adjusting the position of the funnel it could be arranged that each drop fell 

* ' Wied. Annal.,' vol. 46, pp. 584-636, 1892. 

t Blosses Zerstieben des Wassers ist also ebenso unwirksam wie das Hindurchfahren von Strahlen 
durch die Luft; nur Auftreffen getrennter Tropfen auf ein flaches Hinderniss gab stets electrische 
Wirkung. 

3 E 2 



396 



DE. G. C. SIMPSON ON THE ELECTEICITY OF 



upon the jet of air escaping from the nozzle, where it was split up into numerous 
small drops through the sudden stoppage of its downward motion. When this 
adjustment was well made the drops broke up in a symmetrical crown about 4 cm. 
above the nozzle, and the greater part of the small drops so produced fell directly 
into the tray. In order to prevent small spray from being blown over the sides of 
the tray, a roof in the form of a hollow truncated pyramid, having a hole 5 cm. 
square at the top, was fitted over it. The drops fell through the hole in the roof 
and were broken up on the air jet, but only a very little of the spray escaped with 
the stream of air. 




i jj"'l"'j t '"''"iii'" l '"iL'"'""i!i'"'"'ii! ijj ijimli..^.!.!...;!. 

FIG. 2. 

A fine wire-gauze cage was placed over the tray to protect it from extraneous 
electrical fields, and a Dolezalek electrometer was used for measuring the potential of 
the tray. 

The method of making an experiment was as follows. The funnel was filled with 
distilled water and a cock opened to let the water flow in large drops from the 
orifice within the metal cylinder. The bellows were then worked until the 
manometer showed a pressure of about J metre of water and the position of the 
funnel above the nozzle was adjusted until the drops were symmetrically broken up 



EAIN AND ITS OEIGIN IN THUNDERSTORMS. 397 

on the air jet. The box was then connected to earth and a reading taken of the zero 
of the electrometer ; after a convenient interval the earth connection was broken and 
the drops counted as they fell. Readings were taken of the electrometer after each 
100 drops had fallen until 500 had been counted, when the flow of water was 
stopped. The following shows the result of a typical experiment in which distilled 
water was used : 

TABLE VIII. 



No of drops 


100 


200 300 400 


500 




Deflection 


20-0 19-5 


18-8 18-2 17-5 


16-9 




Total deflection = 3-1 cm. = 7'2 volts. 
Hence charge per drop = 


Capacity of system = 87 
4'2 x 10~ 3 els. unit. 


cm. 



Before going any further it will be as well to consider how much of the charge, 
thus measured, could reasonably be ascribed to the breaking up of the drops on the 
jet of air. 

Three possible sources of error have to be considered : 

(a) That the charging might be due to the blast of air alone. 

(b) That the drops might be electrified before being broken up. 

(c) That the effect might be due to the Lenard effect coming into play when the 

drops fell into the tray after being broken up on the air jet ; or in other words, 
that the separation of electricity might not take place when the drops broke 
on the jet, but when they splashed on the water in the bottom of the tray. 

(a) That the blast caused no charging could easily be tested by keeping it in 
action without the drops falling. Frequent experiments were made and showed no 
trace of charging. 

(6) The electrification of the drops was tested by placing a small cylindrical box 
over the air nozzle (as shown by the dotted outline in the figure) to catch the drops 
as they fell. A small hole was made in the side of this box about 2 cm. from the 
bottom, so that a layer of water 2 cm. deep was always in the bottom, and into this 
the drops fell. The Lenard effect would come into play when the drops splashed on 
the water in the box, but as all the electricity separated remained within the tray 
and its lid, this effect could cause no charging of the system. If, however, the drops 
had fallen with a charge on them it would have been detected by a deflection of the 
electrometer. No such effect could be observed. 

(c) In order to prevent the Lenard effect from coming into play when the drops 
fell into the tray after breaking up on the air jet, use was made of the fact discovered 
by LENARD that the splashing of salt water produces the opposite charge to that 



898 



DE. G. C. SIMPSON ON THE ELECTRICITY OF 



given by the splashing of distilled water. A layer of salt water 2 cm. deep was 
therefore placed in the bottom of the tray and into this the drops fell after breaking 
up on the jet. The following test was then made : The funnel was slightly moved to 
the side so that the drops of distilled water fell directly with their full velocity on to 
the salt water on the bottom of the tray, and the blast was also set in action in order 
to remove the air containing any charge separated from the water on splashing, and 
so to produce the largest Lenard effect possible. 
The result was as follows : 

TABLE IX. 



No of drops .... 


100 


200 300 


400 500 










Deflection 


20-0 20 


1 20-2 20-2 


20-3 20-4 




Total deflection = 


0-4 cm. = -0-9 volt. 





This shows that the Lenard effect due to splashing on the bottom of the tray 
produced a slight negative charge, and so it may be concluded that the positive 
charge found in the experiments in which the drops were broken on the air jet was 
not due to splashing on the bottom of the tray. 

It would therefore appear justifiable to assume that the whole of the charge 
measured in the apparatus under discussion was due to the breaking up of the drops 
on the air jet. 

The following table gives the results of six experiments : 

TABLE X. 



Distilled water. 
Volume of each drop = 0'24 c.c. 


No. of drops broken. 


Mean charge produced by a drop 
breaking on the air jet. 


500 
500 
400 
400 
400 
400 


els. unit. 
5-0 xlO- 3 
4-2 x 10- 3 
5-8 xlO- 3 
5 1 x 10- 3 
5-8xlO- 3 
5-8 xlO- 3 


Total . 2600 


Mean . 5 2 x 


io- 3 



RAIN AND ITS OEIGIN IN THUNDERSTORMS. 399 

This result is of the same order of magnitude as that found by LENARD for single 
large drops breaking on a metal obstacle, the charge produced by each drop in these 
experiments being even larger than that found by LENARD in his experiments. 

Experiments were next undertaken to investigate the extent to which the process 
is affected by any charge already on the drops, for it is quite conceivable that charged 
drops might behave quite differently from uncharged drops. For these tests the 
apparatus already described was adapted. It was only necessary to connect the 
cylinder C to a battery, so that each drop which fell from the funnel had a definite 
charge induced on it, and carried it away with it on its fall. The charge carried by 
each drop was found by catching the drops in the small box shown dotted in fig. 2. 
The box was then removed, and the charged drops broken up on the air jet. The 
difference between the total charges measured, with the same number of drops in 
each case, indicated the extent of charging due to the breaking up on the air jet. 

The following gives a typical experiment, in which distilled water was used and 
each drop carried a positive charge : 

TABLE XI. 



Drops caught in little box. 



No. of drops 



Deflection 



100 200 300 400 500 



20-0 17-3 14-3 11-4 8'5 5-7 



Total deflection = 14'3 cm. = +33'5 volts. .'. Charge per drop = 19'5 x 10~ 3 els. unit. 



The small box was then removed, and the drops broken on the air jet. 

TABLE XII. 



Drops broken on air jet. 



No. of drops 





100 


200 


300 


400 


500 
















Deflection 


20-0 


16-5 


13-0 


9-4 


5-9 


2-5 

















Total deflection = 17'5 cm. = 41O volts. .'. Charge per drop = 23'9 x 10~ 3 els. unit. 



Prom these two experiments we find that drops originally positively charged to 
19'5XlO~ 3 els. unit have had this charge increased to 23'9xlO~ 3 els. unit when 
broken up on the air jet, the increase being 4'4x 10~ 3 els. unit per drop. 



400 



DE. G. C. SIMPSON ON THE ELECTRICITY OF 



There is, however, in this result a slight error, due to the fact that when the 
drops break up on the air jet a certain number of the fine drops produced are 
carried upwards with the air stream and so escape out of the measuring system. This 
loss was measured by the use of Simla tap water, which, as has already been 
remarked, was found to be quite incapable of producing a charge, either by splashing 
or breaking up 011 the jet. An experiment was made with tap water charged in the 
same way as in the experiment just considered, and it was found that after breaking 
on the jet the drops had lost part of the charge originally on them, both when the 
charge was positive and when it was negative. The mean value of the loss was found 
to be 5 per cent, of the charge on the drops. 

With drops originally uncharged a 5 per cent, loss was of no particular account, 
the experiments were not accurate to this amount ; but with highly charged drops a 
loss of 5 per cent, of the original charge was appreciable and had to be taken into 
account. 

The following table gives the results of all the experiments made with charged 
distilled water : 

TABLE XIII. 



Distilled water. 


No. of drops broken. 


Mean charge on drop 
before breaking. 


Mean charge due to 
breaking. (Corrected.) 




10~ 3 els. unit. 


10~ 3 els. unit. 


1000 
1200 


+ 19-G 
+ 59-1 


^: 2 6 }c-4 


1000 


-19-5 


+ 4-9"! .. 


1200 


-58-0 


+ 4'5 J 


4400 






Mean . . . . + 5 G 



From this table it will be seen that charged drops obtain a positive charge by being 
broken up on the air jet, and that the magnitude of the charge is approximately the 
same whether the drops are charged positively or negatively. Great accuracy cannot 
be expected in these experiments with charged drops, because the electrometer has 
to be made very insensitive in order to allow of the large charges brought down by 
the drops being measured, and the final result is obtained from the slight variation in 
these large charges caused by the splashing. It is, however, interesting to notice that 
the mean of all the experiments with charged drops gives a mean charge due to. the 
breaking up on the air jet almost equal to that found for uncharged water. 

In Table XIV the results of all the experiments are summed up : 



RAIN AND ITS ORIGIN IN THUNDERSTORMS. 
TABLE XIV. 



401 



Initial charge on drop. 


Electricity added to a drop 
consequence of the breaking 
the air jet. 


in 
on 


10~ 3 els. unit. 

+ 19-6 
-19-5 
+ 59-1 
-58-0 


10~~ 3 els. unit. 

+ 5-2 


Mean . . +5 -5 



As all the drops in these experiments contained approximately 0"24 c.c. of water, 
the charge given to the water is equivalent to a volume charge of 23X10" 3 electro- 
static unit per cubic centimetre of water. 

After making these experiments it was felt that objection might be raised to 
applying the results thus obtained to the breaking up of raindrops in the atmosphere, 
because no such violent scattering of the drops could take place in the atmosphere 
as that obtained when falling drops impinge on a concentrated jet of air. A further 
experiment was therefore devised to produce the breaking up of the drops in a more 
natural way than the one already described. 

The apparatus used is sketched in fig. 3. BB was a vessel made out of tinned 
iron, 65 cm. in diameter and 45 cm. high. In the middle of the bottom was a hole 
7 cm. in diameter, surrounded by a conical rim 7 cm. deep ; thus a layer of water 
7 cm. deep could be put into the vessel without running out through the hole. 
Through this rim passed two small tubes, 0'8 cm. in diameter, which were fitted 
with a simple arrangement for opening and closing them to allow of the passage of 
the water at will. Soldered underneath the main vessel was a smaller one of the 
shape shown in the figure, and around the upper rim a third vessel AA was fixed on 
insulators so that it could be either connected to or insulated from the main vessel B, 
according to the experiment to be made. The whole was supported on insulators in 
such a position that the hole in the centre was directly over but not touching a 
large pipe through which a blast of air could be sent by means of the rotatory fan F. 

When the fan was in action and the tubes open, water passed out through the 
latter in a solid stream into the middle of the air current, by which it was at once 
carried upwards and broken into spray. As the greater part of water carried 
upwards fell back into the main reservoir of water, it could be used over and over 
again. With this arrangement quite large charges were obtained by the vessel B in 
a comparatively short time. For example, the vessel B was connected to A and the 
water allowed to run. The whole system was then found to become charged at the 

VOL. ccux. A. 3 F 



402 DR. G. C. SIMPSON ON THE ELECTRICITY OF 

rate of 20 volts per minute when a rapid blast of air was produced by the fan. This 
rate of charging would have been increased if a large amount of fine spray had not 
been carried from the apparatus by the air current. From the data that the system 
had a capacity of approximately 180 cm. and the water ran out of the tubes at the 
rate of 1200 c.c. a minute it will be seen that the charge given to the water was 
approximately 10 X 10~ 3 electrostatic unit per cubic centimetre, i.e. a charge of the 
same order of magnitude as that produced when individual drops were broken up 
violently on a concentrated air jet. 

As the majority of the drops in this experiment after being carried upwards fell 
back on to a pure water surface, the experiment was not entirely free from the Lenard 
effect. In order to get over this difficulty the large vessel A fitted round the upper 
rim of B was insulated from it. This vessel caught a certain amount of the fine 
spray thrown up by the blast, and as the drops were exceedingly small and were 
only just beginning to fall when they were caught, they struck the sides of the 
vessel A without sufficient momentum to cause splashing ; it was therefore concluded 
that very little separation due to the Lenard effect could take place at the impact. 
The vessel B was then connected to earth, and A to a Wilson electroscope, and the 
water and blast set into action. When the electroscope measured a definite potential 
the blast and water were stopped, and the quantity of water caught in the vessel A 
was run off and measured. 

The following shows the results obtained in a series of experiments in which rain- 
water was used and the system was allowed to charge itself up to 9 volts before 
measuring the water collected in A : 

Amount of water 
caught in A. 

1st experiment 300 c.c. 

2nd 280 

3rd 290 

4th 230 

5th 265 

Mean 273 

Capacity of system = 135 cm. 

.'. Charge on 273 c.c. of water = ^ -els. units. 
i.e. Charge per c.c. of water = 15X10~ 3 

Thus the charge per cubic centimetre of water is of the same order of magnitude as 
that found when single drops were violently broken up on the air jet, and is only 
slightly smaller in amount. From these experiments it would appear safe to 
conclude that when pure water is broken up from large to small drops in the air 
under ordinary conditions of temperature and pressure a ' separation of electricity 
takes place. 



RAIN AND ITS ORIGIN IN THUNDERSTORMS. 



403 



In all the experiments described hitherto the amount of separation has been 
measured by means of the charge retained on the water. Experiments were now 
undertaken to see if the charge carried away by the air could be measured. 

The experiment was arranged as indicated in fig. 4. AA was a zinc cylinder 
8 '5 cm. in diameter and 60 cm. long. Its lower end fitted into a glass taken from 
a " hurricane lamp," which in turn fitted into another small cylinder as shown at B. 
Through the bottom of the lower cylinder a glass tube drawn out to an orifice about 
2 mm. in diameter at its upper end projected into the middle of the glass, and 
through this orifice a jet of air was passed in a way similar to that described in the 
previous experiments (see fig. 2, p. 39G). 





ici at, aw " 40 io eo 10 so eo 
1 m.lro 



FIG. 3. 



FIG. 4. 



From a tube D at the top of the cylinder AA drops of water fell on to the jet of 
air and were broken up into small drops by the impact. In order to test the air of 
the jet on which the drops were broken for an electrical charge, an Ebert apparatus 
was connected to the cylinder AA through a short tube E fixed about 5 cm. above 
the place where the drops were broken. When the fan of the Ebert apparatus was in 
action it drew air through holes in the top of the cylinder AA which swept the air of 
the jet with it through the Ebert apparatus. ' The experiments were made as follows : 

The central cylinder of the Ebert apparatus was charged to a potential which could 
be read by the divergency of the leaves of the attached electroscope. The air of the 
jet was then put into action, and a reading of the electroscope taken. The fan was 
then allowed to draw air through the instrument for 10 minutes, when a second 
reading of the electroscope gave the loss of electricity due to the natural ionisation of 

3 F 2 



404 



DE. G. C. SIMPSON ON THE ELECTRICITY OF 



the air in that period. Drops were then allowed to fall from the tube D on to the jet, 
and two more readings of the electroscope were taken with intervals of 10 minutes 
between them, and the number of drops which had fallen in that time was noted. The 
difference of the results of the two experiments gave the amount of electricity imparted 
to the air by the breaking of a known number of drops, and from this the amount due 
to the breaking of a single drop was calculated. Similar experiments were made with 
the central cylinder of the Ebert apparatus charged both positively and negatively. 
The results are shown in the following table : 

TABLE XV. 



Distilled water. 


Sign of charge 
of air. 


Loss of volts 
in 10 minutes 
with air jet 
without 
drops. 


Loss of volts 
in 10 minutes 
with drops 
being broken 
on air jet. 


Loss of volts 
due to the 
breaking of 
the drops. 


No. of drops 
broken in 
10 minutes. 


Loss of volts 
due to 
breaking of 
one drop. 


Mean of 
two 
experiments. 


Negative . . 
Negative . 


1-1 
1-9 


30-3 

27-9 


29-2 
26-0 


394 
384 


0-074 
0-065 


| 0-071 


Positive 
Positive . . 


2-0 

2-7 


12-3 

10-8 


10-3 

8-1 


385 

411 


0-027 
0-020 


| 0-024 



Now, as the capacity of the Ebert apparatus was 14 els. units 
The mean negative iouisation caused by the 
breaking of one drop 



= " = 0'0033 els. unit. 



- = O'OOll els. unit 



The mean positive ionisation caused by the 

breaking of one drop ....... 

Excess of negative ionisation caused by the 

breaking of one drop ....... = 0'0033 O'OOll = 0'0022 els. unit. 

The results of these experiments are interesting, in that they show 

(1) The breaking of drops of water is accompanied by the production of both positive 

and negative ions.* 

(2) That three times as many negative ions as positive ions are released. 

The difference between the negative and positive charges produced should correspond 
to the charge remaining in the water. Now, it has been shown above that 5 - 5X 10~ 3 
els. unit of positive electricity is retained by the water of each drop after breaking, 
and this amount agrees as well as could be expected with the 2'2XlO~ 3 els. unit 
per drop found in the air ; the difference is no doubt due to the fact that many of the 

* This experiment does not indicate the nature of the ions produced : for instance, the positive ions 
might be exceedingly fine water drops. Still it shows that something of the nature of ordinary ionisation 
takes place and that the ions exist long enough to be separated by the Ebert instrument. 



RAIN AND ITS ORIGIN IN THUNDERSTORMS. 



405 



tions given to the air at the splashing of the water are not drawn into the Eber 

instrument, but give up their charges to the sides of the apparatus. 

The results of these experiments may be summed up in the following sentence : 
When water drops are broken up in the atmosphere a separation of electricity 

takes place, the water becomes positively charged, and the air negatively charged ; 

and further, the amount of separation is independent of any charge previously on the 

drop. 

PART III. -Theoretical Conclusions. 

The consideration of the electricity of thunderstorms, which was the starting point 
for the experiments just described, will now be resumed. It has been pointed out that 
if the breaking of the raindrops in the air were accompanied by a separation of 
electricity, this property might be the cause of the electrical effects observed during 
thunderstorms, and it now remains to ascertain the extent to which . this suggestion 
can be developed into a satisfactory explanation of the phenomena of thunderstorms. 

In order that the explanation may be satisfactory it is necessary to show 

(1) that there is a considerable breaking up of raindrops during a thunderstorm. 

(2) That the quantity of electricity which could be developed in this way is sufficient 

to account for the electrical effects observed. 

(3) That the general meteorological conditions which usually accompany thunder- 

storms agree with the explanation. 

Turning now to the first of these requirements, it will be shown that in all probability 
the rainfall of thunderstorms is accompanied by considerable breaking up of large 
into small drops. This can best be done by considering Prof. LENARD'S article 
on " Rain,"* already referred to. 

Prof. LENARD made a number of experiments to determine the final velocity 
attained by drops of water of different sizes when falling through air. His experi- 
mental method was to create a vertical current of air and find the velocity of the 
current which was just able to support drops of a given size. The following table 
gives the results obtained : 



Diameter of 
the drops. 


Velocity of the air which supported the drops 
= the filial velocity of the drops in still air. 


Observed. 


Calculated. 


mm. 
1-28 


Metres per second. 
4-8 


Metres per second. 
5-65 


3-49 


7-37 


9-3 


4-50 


8-05 


10-6 


5-47 


7-98 


11-7 


6-36 


7-80 


12-6 



* LENARD, 'Met. Zeit.,' vol. 21, pp. 249-262, 1904. 



40(5 DE. G. C. SIMPSON ON THE ELECTEICITY OF 

About this table Prof. LENARD says : " One sees from it that the velocity quickly 
reaches a limiting value as the size of the drops increases (very nearly equal to 
8 metres a second), above which it does not increase ; it even decreases a little as the 
drops grow still greater." 

He then showed that this apparent anomaly is due to the drops becoming deformed, 
so that instead of retaining the shape of spheres they become flattened out, thus 
presenting an increased resistance to the air through which they fall. In consequence of 
this deformation large drops rapidly break up in the air into smaller drops, and 
LENARD found that drops of 4 mm. diameter were stable under all conditions, but that 
drops 5'5 mm. and above in diameter could not exist for more than a few seconds after 
attaining their final velocity relative to the air. 

This fact plays an important part when drops of water are falling tl iron gli ascending 
currents. According to the table given above, all drops of water of a smaller diameter 
tlian 4'f> nun. will be carried upwards by a current of 8 metres a second, while 
all drops of a larger diameter than this will be held in suspension, neither rising nor 
falling. Hut the latter are unstable, and after floating for a few seconds in the 
current break ii]> into small drops which are carried upwards. Thus no water could 
possibly fall through an ascending current of air having a velocity of 8 metres a 
second or more. 

That thunderstorms are accompanied by strong ascending currents is admitted 
by all meteorologists, but I know of no actual measurements of the ascending 
currents within a thundercloud ; still the question can be discussed from indirect 
evidence. 

Then; is no essential difference in kind between a tornado, a hailstorm, and an 
ordinary thunderstorm, all of which are accompanied by electrical discharges. 

Now in the first two of these we know definitely that ascending currents of 
excessive velocity do occur. The many authenticated cases in which heavy structures 
and implements have been raised to considerable heights during tornadoes give 
absolute proof of ascending currents comparable with the greatest horizontal winds 
known. Now a horizontal velocity of 8 metres a second (29 kilometres, or 18 miles 
an hour) is defined as a moderate breeze, and wind velocities of 40 metres a second 
(approximately 100 miles an hour) have been measured during tornadoes; thus we 
see that ascending currents having velocities many times greater than 8 metres 
a second must occur during tornadoes. 

In the formation of hailstones we have equally certain evidence of strong ascending 
currents. A hailstone cannot grow appreciably above the size which would be 
sufficient to cause it to fall to the ground through the ascending currents below it, so 
that the size of a hailstone gives a rough measure of the upward velocity of the air 
current in which it was formed. Now hailstones have been met with having all sizes 
between those of peas and those of melons. A hailstone as big as a pea would 
require a vertical velocity of at least 10 metres a second to hold it in suspension ; 






RAIN AND ITS ORIGIN IN THUNDERSTORMS. 407 

thus the ascending currents which produce stones as large as oranges and melons 
must be enormous. 

It would therefore appear that those disturbances in the atmosphere which are 
accompanied by the greatest amount of electrical discharge are also accompanied by 
violent ascending currents, much larger in all cases than the 8 metres a second 
necessary to hold water in suspension, and so it cannot be considered to be an 
unwarrantable assumption that in all thunderstorms a velocity of 8 metres a second 
occurs. 

A strong vertical current in the atmosphere must have a form something like that 
of an hour-glass, having a comparatively large cross-section at the bottom where 
horizontal currents are feeding into it, and spreading out at the top to allow of the 
escape of the air after ascension. For simplicity in the following discussion we will 
imagine an ascending current to consist of three parts : (a) a base in which the cross- 
section is large and the vertical velocities are small ; (6) a column of ascending air of 
which the cross-section is comparatively small and the vertical velocities are large 
and more or less constant throughout ; (<) a cap or crown in which the air rapidly 
spreads out in all directions so that the vertical velocities are very small a short 
distance above the head of the column. If the air in the base is saturated, then as it 
rises through the column it will have its temperature reduced at the rate of 
approximately 0'5 C. for eacli 100 metres of ascent, and there will be considerable 
condensation of water, which will form drops and tend to fall. If, however, the 
vertical velocity within the column is 8 metres a second or over" no water can fall, but 
it will all be carried upwards until it readies the top of the column, where the 
vertical velocities diminish. Here the water will accumulate in the form of drops 
which will continually be going through the cycle of growing to 5'5 nun. in diameter 
and then being broken up into a number of small drops, each of which will grow 
again. A rough approximation of the rate at which the water accumulates can be 
formed by assuming certain simple conditions. Thus let us assume that the height 
of the column is 2000 metres, so that the air which enters the base will be cooled 
10 C. during the ascent, and let the initial temperature be 15 C. Then by the time 
the air reaches the top approximately 6 grammes of water will have been precipitated 
within each cubic metre of air, and if all this accumulates at the top of the column,* 
6X8, or 48, grammes of water will have collected over every square metre of the 
column in one second, that is, in 10 minutes the water accumulated would be 
equivalent to a layer of water 2'9 cm. deep, or if the water is in the form of drops 
there would be at the end of 10 minutes 36 drops, each of the maximum size of 
5'5 cm. diameter, over every square centimetre of the cross-section. Thus if the 

* This of course is only assumed for purposes of a rough approximation ; it is not intended to assert 
that all the water carried up by the current would accumulate at the top of the column, but as the 
accumulation which would result from rain falling from above has been neglected, the calculation will give 
some idea of the magnitudes with which we are concerned. 



408 DR. G. C. SIMPSON ON THE ELECTRICITY OF 

ascending current had a velocity of only 8 metres a second enough water would be 
deposited for a considerable breaking up of drops. 

Turning now to the second point which the theory has to consider, a rough 
estimate will be made of the amount of electricity which could be separated under 
such conditions. For this purpose it will be necessary, in order to simplify the 
reasoning, to make several somewhat artificial assumptions. It will be assumed that 
the ascending current extends over a fairly large area, so that vertical distances may 
be considered as small in comparison with horizontal ones ; that the separation of 
electricity takes place uniformly over a horizontal plane ; and that all the positive 
electricity remains in the water near the place of separation, while all the negative is 
carried vertically upwards in the air stream. We will first consider how many drops 
must be broken in order to set up the potential gradient of 30,000 volts per 
centimetre which is necessary for a lightning discharge. This field is set up between 
two parallel plates having a surface density of 8 els. units per square centimetre. 
Thus sufficient drops must break over each square centimetre to provide 8 els. 
units before a discharge can take place, and as the breaking of each drop 

Q 

provides 5X 10~ ;t els. unit, this will occur when ,, or 1GOO, drops have broken. 

u X 1 U 

Thus if 1 drop breaks over each square centimetre every second, a discharge can 
take place after 27 minutes; or, if 27 drops break, after 1 minute. Now it has 
already been shown that under certain conditions which are not at all improbable, 
30 drops of water, eacli large enough to be broken up, will have accumulated in the 
course of 1 minutes over eacli square centimetre of the ascending current ; hence, 
it does not seem at all improbable that with even moderate values of the ascending 
current sufficient breaking of drops could take place to give the rapid electrical 
discharges observed in thunderstorms. In this connection it is important to realise 
that each electrical discharge in a thunderstorm only neutralises the electricity over 
a small area of the region in which separation takes place. Thus suppose that the 
ascending current is 4 kilometres in diameter, and that each discharge neutralises the 
charge over 1 square kilometre of area, then it would take 12 discharges to neutralise 
the whole electricity over the whole surface. Under these conditions, if the potential 
gradient were being created at the rate of 30,000 volts per centimetre every minute, 
the lightning discharges would occur on the average every 5 seconds. 

It may also be considered how many times a given mass of water would have to 
be broken up in order to give to the rain which falls from the cloud the charges of 
electricity which are actually measured. The case of rain positively charged will 
be considered first. From Table III, p. 388, it will be seen that the positive 
charge carried down by the rain is of the order of magnitude of 1 els. unit per cubic 
centimetre of water. The laboratory experiments showed that water which has 
splashed once has a charge of the order of magnitude of 10 X 10~ 6 els. unit per cubic 
centimetre. Thus the water on the average would have to splash something like 



RAIN AND ITS ORIGIN IN THUNDERSTORMS. 409 

100 times to give the charges measured. There is no reason for considering that this 
would be impossible with violent and widespread ascending currents. 

The air which passes through the accumulation of water at the head of the 
ascending current carries with it the negative electricity separated during the 
splashing. This electricity is rapidly absorbed by the cloud particles through which 
the air streams in its upward course, and it is very probable that large negative 
charges could in consequence be accumulated in the cloud. Thus the cloud over the 
ascending current will consist of negatively charged water particles, and these will 
coalesce to form rain having a negative charge. There is no means of estimating 
what negative charge might be expected, but there is no reason for considering that 
it should be smaller than the positive charge brought down by the water which 
has been broken up several times at the head of the ascending current. Thus it 
would appear that the process could provide both the positively and negatively 
charged rain actually observed. 

The quantitative estimate which lias just been made has been based on values 
which cannot be considered as being anything more than the roughest approximations. 
It shows, however, that it is not necessary to assume ascending currents of more than 
8 metres a second to supply enough electricity for a considerable amount of lightning 
discharge, and that given reasonably rapid ascending currents, sufficient separation of 
electricity could take place to account for the most violent thunderstorms. 

The preceding discussion will now be summed up in an account of the probable 
mechanism of a thunderstorm. 

When extensive ascending currents occur in air which is not exceedingly dry, the 
formation of cumulus clouds with possible precipitation will naturally follow. As 
the ascending currents become more and more rapid large amounts of water will be 
held in suspension, until finally, when they attain a greater velocity than 8 metres 
a second, all water will be retained. As a consequence there will be considerable 
breaking up of drops in the air accompanied by a separation of electricity, by which 
the water becomes positively charged and the air negatively charged. 

The electrical effects react on the rate of splashing. Uncharged drops combine 
only with difficulty, and rebound from one another as though they were solid. 
Charged drops, on the contrary, combine with facility to form single large drops.* 
Thus as the water becomes more and more highly charged the drops will the more 
rapidly grow to the size necessary for them to be broken again, and as a 
consequence the greater will be the splashing and the greater the rate of electrical 
separation. 

An ascending current must at some place in its ascent spread out horizontally and 
so have its vertical velocity reduced. At the part of the current where the velocity 
falls below 8 metres a second a large accumulation of water will in all probability 
take place, and this will be the seat of the greatest amount of separation of 

* RAYLEIGH, 'Roy. Soc. Proc.,' vol. 28, p. 406, 1879. 

VOL. CCIX. A. 3 G 



410 DR. G. C. .SIMPSON ON THE ELECTRICITY OF 

electricity. Now where the vertical current spreads out horizontally the stream 
lines of the air have horizontal components. For the present purpose it does not 
matter whether we consider that the vertical current spreads out uniformly on all 
sides or is deflected in a certain direction. In either case the water accumulated at 
the head of the current will be gradually moved horizontally until it reaches the 
edge of the rapid vertical current, and there it will be able to escape by falling ; but 
as it will necessarily take some time for any given mass of water to travel from the 
centre to the outside of the ascending current, there will be time for considerable 
breaking up before the drops actually fall. Thus the water carried up by the 
ascending current will fall as positively charged heavy rain over one or other of the 
edges of the ascending current. This is of course considering the case in its simplest 
terms. As a matter of fact, the ascending current will vary in velocity, will have 
its gusts and lulls just as a horizontal wind has. Such variations, however, will be 
of great help in causing splashing, for LENARD* found that " the sudden contact of 
already deformed drops with a quicker air stream is very favourable to the breaking 
of the drops." Another consequence of the gusts and lulls in the ascending currents 
will be the raising and lowering of the region in which the water is held in 
suspension, and with this will follow rapid changes in the electrical field which may 
possibly help to produce electrical discharges. 

The water which has become positively charged on the ascending current and then 
fallen as rain will be the heavy rain which occurs in the centre of the thunderstorm : 
the ' Platzregen " of the German authors. In view of this consideration, it will be 
interesting to look at the results of actual measurements of rain electricity, to see if 
the heavy rain which falls in the centre of a thunderstorm is positively charged. 
There are four sets of measurements of rain electricity which can be used for the 
purpose, viz., those of ELSTER and GEITKL'S first series of experiments, published in 
the ' Wiener Berichte ' ; their second series, published in ' Terrestrial Magnetism and 
Atmospheric Electricity ' ; those of WEISS, published in the ' Wiener Berichte ' ; and 
finally those in this paper. 

These will be taken in the reverse order, and the Simla measurements considered 
first. It has already been pointed out in the first part of this paper (p. 390), that in 
every one of the 97 cases in which the rainfall equalled or exceeded 0112 cm. in 
two minutes the rain was positively charged. 

WEISS f does not record any case of a thunderstorm, nor do rainfalls so large as 
those just described occur in his observations ; but nevertheless he made observations 
during two rain squalls (" Regenboe," Tables 12 and 14), and he states that in the 
former " Platzregen " fell ; from his tables it will be seen that this excessive rain 
was positively charged (Nos. 182-184 of Table 12). In the second "Regenboe" the 
rain was positively charged throughout. 

* Loc. ci(., p. 256. 

t WEISS, ' Wien. Ber.,' vol. 115, p. 1285, 1906. 



RAIN AND ITS ORIGIN IN THUNDERSTORMS. 411 

ELSTEE and GEITEL'S* observations, recorded in ' Terrestrial Magnetism and 
Atmospheric Electricity,' give the same result. In the article referred to no tables 
are given, but 17 figures show the results of the observations. In four of these 
figures (figs. 2, 7, 10, and 17) we find " Platzregen" recorded, and in each case high 
positive charges accompany the heavy rain. 

The only exceptions to this general rule are to be found in ELSTER and GEITEL'S! 
first paper on the electricity of rain, published in the ' Wiener Berichte ' for 1890, in 
which we find that the " Platzregen " is more often accompanied by negative than 
positive electricity. In view of all the other observations, which show without 
exception the positive charge of " Platzregen," it is difficult to explain this 
discrepancy ; biit, accepting it in full, it may still be said that the evidence in favour 
of the view that the excessive rain within a thunderstorm is positively charged is 
overwhelming. 

Advancing a step further, it will be necessary to consider what happens to the 
negative electricity which is separated when a drop breaks up. It is very probable 
that this charge is given to the air in the form of free negative ions, and it appears 
certain that these will, on formation, be carried upwards with the full velocity of 
the ascending air ; they will then quickly leave behind the drops of water which 
retain the positive electricity. 

But the negative charge cannot exist long as free ions, for the latter will be rapidly 
absorbed by the cloud particles with which the air is filled. In this way the cloud 
particles may become exceedingly highly electrified. Now within a highly electrified 
cloud there must be rapid combination of the water drops, and from it considerable 
rain will fall : this rain will be negatively charged, and, under suitable conditions, 
both the charge on the rain and the rate of rainfall could be large. But it is 
important to notice that the negatively charged rain has an entirely different origin 
from that of the positively charged rain, and therefore the character of the rainfall 
might be expected to be different in the two cases. It has already been shown that 
the positively charged rain is likely to occur in heavy downpours in consequence of 
its intimate connection with the ascending currents, but as the negatively charged 
rain is formed in the large cloud masses, which are more or less uniformly charged 
and extend over and around the ascending currents, the negatively charged rain is 
likely to have a much more uniform rate of fall, and also to occur in the intervals 
between the bursts of the positively charged rain. 

The observations bear out these considerations in a remarkable way. In storm 
after storm it was found that negatively charged rain fell in the lulls after a heavy 
downpour of positively charged rain. Negatively charged rain never occurred in 
heavy downpour, but was very often associated with steady rain from a lightly clouded 
sky. Also negative electricity was measured but rarely, and in large quantities 

* ELSTER and GEITEL, 'Terr. Mag. and Atm. Elect.,' vol. 4, pp. 13-32, 1899. 
t ELSTER and GEITEL, ' Wien. Ber.,' vol. 99, p. 421, 1890. 

3 G 2 



412 DR. G. C. SIMPSON ON THE ELECTRICITY OF 

never, in the regions of the storms in which violent and frequent lightning discharges 
occurred. 

It will sometimes happen that the negatively charged cloud will be carried by the 
upper winds to some distance from the place where the separation of electricity was 
effected and will then give rain. In such cases, rain charged with negative electricity 
would be likely to occur. The frequency with which negative electricity was 
observed by ELSTER and GEITEL with rain associated with distant thunderstorms 
might be explained in this way. 

If the ascending current keeps a considerable amount of the highly charged water 
in suspension, and the negative electricity is held in the cloud above, it is very 
probable that the main lightning discharges would take place from the accumulated 
water at the head of the ascending current to the charged cloud above. This 
would explain the observation that most lightning discharges pass within the 
thundercloud from base to summit. 

Falls of hail are frequently associated with thunderstorms, and hailstones as has 
already been pointed out can only form if they are supported during formation 
by strong ascending currents. Further, the structure of a hailstone indicates that it 
is often carried up and down past the zero isothermal. Now, a current of air 
sufficiently strong just to support a hailstone as big as a pea would be more than 
sufficient to carry up the water it condenses within itself; hence, hailstones would 
always have a greater downward velocity relative to the ascending current than the 
water in the current, and there would be a large amount of splashing between 
the two. There would be, consequently, a much greater amount of separation 
of electricity than would have taken place without the hailstones, and this 
might very well account for the great violence of the electrical discharges in hail- 
storms. 

The observations made by Mr. CLAYDKN* on the formation of thunderclouds seem 
to me to be in entire agreement with the general disposition of air currents required 
for the theory here proposed. 

The present discussion is confined to the electrical phenomena of thunderstorms, as 
I have not yet collected data which are sufficient to allow me to decide whether in 
steady rain such as accompanies ordinary depression, positive or negative electricity 
predominates. It is quite conceivable that the charge brought down under such 
conditions is due to causes entirely different from those which produce the excessive 
electrical separation in thunderstorms. For similar reasons the electrical phenomena 
connected with snowstorms have not been considered. Until all these effects have 
been studied it is not possible to discuss the bearing of my observations on the general 
problem of atmospheric electricity. 

The investigation of vertical air currents during a thunderstorm would have an 

* Loc. tit,, pp. 109,110. 



RAIN AND ITS ORIGIN IN THUNDERSTORMS. 413 

important bearing on the questions discussed in this paper. A simple method might 
be based on a comparison of the rates of ascent of balloons during normal weather and 
during thunderstorms. The retardation due to the water attaching itself to the 
balloon would have to be estimated, but in spite of the uncertainty arising from this 
cause, valuable information would probably be obtained by a systematic series of 
observations. 



[ 415 ] 



XVI. Functions of Positive and Negative Type, and their Connection with the 

Theory of Integral Equations. 

By J. MERCER, B.A., Trinity College, Cambridge. 
Communicated by Prof. A. R. FORSYTH, Sc.D., LL.D., F.R.S. 

Received December 21, 1908 Read May 13, 1909. 

Introduction, 

THE present memoir is the outcome of an attempt to obtain the conditions under 
which a given symmetric and continuous function K (.s, t) is definite, in the sense of 
HILBERT.* At an early stage, however, it was found that the class of definite 
functions was too restricted to allow the determination of necessary and sufncie?it 
conditions in terms of the determinants of 10. The discovery that this could be 
done for functions of positive or negative type, and the fact that almost all the 
theorems which are true of definite functions are, with slight modification, true of 
these, led finally to the abandonment of the original plan in favour of a discussion of 
the properties of functions belonging to the wider classes. 

The first part of the memoir is devoted to the definition of various terms employed, 
and to the re-statement of the consequences which follow from HILBERT'S theorem. 

In the second part, keeping the theory of quadratic forms in view, the necessary 
and sufficient conditions, already alluded to, are obtained. These conditions are then 
applied to obtain certain general properties of functions of positive and negative type. 

Part III. is chiefly devoted to the investigation of a particular class of functions of 
positive type. In addition, it includes a theorem which shows that, in general, from 
each function of positive type it is possible to deduce an infinite number of others of 
that type. 

Lastly, in the fourth part, it is proved that when K (s, t) is of positive or negative 
type it may be expanded as a series of products of normal functions, and that this 
series converges both absolutely and uniformly. 

* <G6tt. Nachr.' (1904), Heft I. 
VOL. CCIX. A 456. 18.10.09 



416 ME. J. MEECEE: FUNCTIONS OF POSITIVE AND NEGATIVE TYPE, 

PART I. DEFINITIONS AND DEDUCTIONS FROM HILBERT'S THEOREM. 

1. Let K(S, t) be a continuous symmetric function of the variables s,t which is 
defined in the closed square a < s ^ b, a < t : b ; and let <s> be the class of all functions 
which are continuous in the closed interval (a, l>). When the function ranges 
through the class , there are three possible ways in which the double integral 



\ K (s,t)e(s)6(t)dsdt. 

J a J a 

may behave : 

(i) There may be two members of 6, say t and 6 2 , such that 

f f K (x, t) 6, (s) e i (t) ds dt, \" l K (s, t) 6, (s) 2 (t) ds dt 

J a J a J a J a 

have opposite signs ; 

(ii) Each function may be such that 

f f K (s,t)0()8(t)d#dt>Q; 

* a " 'a 

(iii) Each function may be such that 

K (s, t) 6 (s) 9 (t.) <!x (It < 0. 

This suggests a classification of continuous symmetric functions defined in the 
closed square. We shall speak of those which have the property (i) as functions of 
ambiguous type, whilst the others will be said to be of positive or negative type, 
according as they satisfy (ii) or (iii). 

2. From the point of view of integral equations this classification is of considerable 
importance. HILBERT has proved* that 



\" f K (s, t) (s) (0 ds dt = S 1 [7 ^ (*) (s) 

la- a = ] A n |_* a 



where ^ (s), t// 2 (), ..., />($), ..., are a complete system of normal functions relating to 
the characteristic function K (s, t) of the integral equation 



and \i, X 2 , ..., X n , ..., respectively, are the corresponding singular values. It follows 
at once from this that, when the singular values are all positive, K (s, t) is of positive 

* 'Gott. Nachr.' (1904), pp. 69-70. See also SCHMIDT, 'Math. Ann.,' Band 63, pp. 452, 453. We 
shall refer to the result given above as HILBERT'S theorem. The theorem stated by HILBERT on p. 70 of 
the paper referred to can be deduced by writing (s) = x(s) + y (s) in the equation written above. 



AND THEIR CONNECTION WITH THE THEORY OF INTEGRAL EQUATIONS. 417 

type in accordance with the above definition. Conversely, we may prove that, for 
every function of positive type, the above integral equation has only positive singular 
values. For, if we multiply along the homogeneous equation 



by / (s), and integrate with respect to s between the limits a and b, we obtain 



Since the double integral on the left cannot be negative, and X n is a finite number, 

it appears that 

A_>0. 

Thus the necessary and sufficient condition that a continuous symmetric function 
should be of positive type is that the integral equation of the second kind of which it is 
the characteristic function should have all its singular values positive.* 

In a similar manner it may be proved that this statement remains true when we 
replace the word positive by negative, in both places where it occurs.* Moreover, 
since a function must be of ambiguous type when it is of neither the positive nor the 
negative type, we conclude that the necessary and sufficient condition for a continuous 
symmetric function to be of ambiguous type is tlie existence of botfi, positive and 
negative singular values of the integral equation of the second kind of which it is the 
characteristic function. 

3. It is easy to see that, corresponding to a function K (s, t) whose type is 
ambiguous, there exists a function 9 (s) which is not zero in the whole interval (a, b), 
and satisfies the relation 



K(s,t)0(s)6(t)dsdt = ........ (A) 

J a J a 

For, if we employ the notation of (i) above, and suppose that k is any real constant, 
we shall have 

f f K (s, t) [0, (s) + k0, (s)] [0! (t) + k6, (0] ds dt = P I* K (s, I) O l (s} 9, (t) ds dt 

Ja Ja Ja J a 

+ k f | ' K (s, t) [0, (s) 2 (t) + 2 (s) 6, (t)] ds dt + F f f K (s, t) 2 (s) 0. (t) ds dt. 

J a J a Ja J a 

* It follows from these results that, unless K (s, t) is identically zero, we cannot have 

I " K (s, t) 6 (s) 6 (f) ds dt = 0, 

for all members of 6. We shall prove this result in a different manner further on ( 12), but it is useful to 
make the remark at this stage, since it shows conclusively that a function which is not identically zero 
cannot be both of positive and negative type. 

VOI,. OCJX. A, 3 H 



418 MR. J. MERCER: FUNCTIONS OF POSITIVE AND NEGATIVE TYPE, 

The coefficient of F on the right has a sign opposite to that of the term independent 
of k ; accordingly, when we equate the right-hand member to zero, the resulting 
quadratic has its roots real. It follows that, if we suppose one of them to be a, the 
function 



will satisfy (A), and it cannot be identically zero, because this would imply that 6 l (s) 
is a constant multiple of 2 (s), and hence that the two integrals mentioned in (i) have 

the same sign. 

The converse of this theorem, however, is not true, for there are functions both of 
the positive and of the negative type which agree in this property with those of 
ambiguous type ; these are known as the semi-definite functions. The remainder are 
called definite functions, and have the property that (A) can only be satisfied by a 
function (x) which is zero at each point of (a, 1>). 

The two classes of functions we have just mentioned have distinctive properties in 
the theory of integral equations. For, if K (x, t) is of positive or negative type, it is 
evident from HJLBERT'S theorem that (A) can only hold when 

(*)0()cfo = (n= 1,2, ...) 

By a known theorem* we must, therefore, have 

' K (.s, t) (>) (It = (a < s < b). 

(I 

Thus the. nec-es*<u-tj diid sufficient condition t/iat a function of positive or negative 
type sh-ould be definite is that it should be perfect. 

PART Tl. THK NATURE OF FUNCTIONS OF POSITIVE AND NEGATIVE TYPE. 

4. The double integral 

"('/<(, i) (x) (t) ds dt, ........ (1) 

- a J a 

in which K (s, t) is an assigned symmetric and continuous function, and 6 is any 
member of the class B, may be regarded as the limit of a certain set of quadratic 
expressions. For, let a,, 2 , ..., a n be points of the interval (a, b), taken in such a 
way that the distances between consecutive members of the set of points consisting of 
a, b and these n are all equal. Then, by the theory of double integration, and in 
virtue of the symmetry of K (s, t), (1) is precisely equal to 

(b -a) 2 Lt [ K ( a i' 
* 



n 2 



* Of. SCHMIDT, op. cit., pp. 451, 452, 



AND THEIR CONNECTION WITH THE THEORY OF INTEGRAL EQUATIONS. 419 

The quantity inside the square brackets is evidently a particular value of a 
quadratic form whose coefficients are K(a 1 ,a l ), /f(a a , 2 ), * (^, ), 2* (MI, 2 ), ... ; 
and, when ranges through the class 0, the numbers (a,), 0(a 2 ), ..., #() will 
assume all possible real values. 

It is thus suggested that we are to look upon the double integral(l), when Granges 
through , as the limiting case of a quadratic form whose variables assume all possible 
real values. The function K(S, t) clearly takes the place of the coefficients of the 
form. Moreover, when K(.S, t) is of positive type, the double integral (I) corresponds 
to a quadratic form which cannot take negative values for real values of the variable ; 
and similarly in regard to the case when K (*, t) is of negative type. 

Now the question, whether a quadratic form does, or does not, take both signs, as 
the variables assume all real values, has been shown to depend on the signs of certain 
determinants whose elements are coefficients of the form.* The considerations we 
have just indicated seem, therefore, to point to the existence of properties of the 
function K (.s, t) which will decide its type, without directly considering the integral 
(1). It is the object of the present section to show that this is actually the case. 

5. Let us, for the present, confine our attention to a function K (.s-, t) of positive 
type, so that 



for all functions 6 belonging to 8. 

We shall, in the first place, define a particular class of the functions B. Let s l be 
any point of the open interval (<i, 6), and suppose that e and -q are any two positive 
numbers which are so small that the points A' 1 (^ + e) also belong to the interval. 
Then the continuous function which is zero for a < a S- i rj e and SjH-ij + eSEs 2E 6, 
which is equal to unity for KITJ -s* 2= *i + r}, and winch is a linear function of .s in the 
intervals (s l T? e, s, 17), (.S^ + T?, Xi + rj + e), will be denoted by &,^(* ; *i). The values 
of the function in these latter intervals will be given by 



respectively, and will evidently be positive numbers less than unity at interior points. 
Consider now the values of the function 



at the various points of the square a^s^b, a^t^b oi the (s, t) plane. In the 
accompanying figure this large square, which we shall denote by Q, is intersected by 

* See, for example, BROMWICH, ' Quadratic Forms and their Classification by means of Invariant 
Factors' (1907), chap, ii., where necessary conditions are obtained. It is not difficult to obtain conditions 
which are both necessary and sufficient. 

3 H 2 



420 MR. J. MEitCEfc: FUNCTIONS OF POSITIVE AND NEGATIVE TYPE, 

two sets of four lines drawn parallel to the axes of s and t; these are the lines 
t = s l 7 ) , * = a 1 (iy + e); = *ii7, a = i(i7 + ) respectively, and they may be 
identified by observing that the number at the point where any one of them 
intersects an axis is the value of the corresponding variable which is constant along 
it. It will thus be seen that the square denoted by q n is bounded by the four lines 



S|_J|J 

c*x. 



H 



10 



AXIS OF S 



Fig. 1. 

s = SJ + TJ, f = Si + r) ; while the area d n , which is shaded in the figure, and which will 
be referred to as the border of q n , is the part of the square bounded by s s 1 (? + ), 
t Si (17 + e) exterior to q n . A. little reflection will show that, at points of Q which 
do not belong either to q u or to d u , one or other of the functions d tiJI (s ; s^, B,^(t; s) 
is zero ; that, at points of q u , each of these functions is unity ; and, finally, that in d u 
neither function exceeds unity. It follows then that 



6. The integral 



= 1 in q u , 
S 1 in d n , 
= elsewhere. 



f K(s,t)e, i1l 

> a 



AND THEIK CONNECTION WITH THE THEORY OF INTEGRAL EQUATIONS. 421 

may be looked upon as K(S, t) 6 ltri (s ; Si) 0, ir ,(t ; s l )(dsdt) taken over Q, or, as it is 
usually written,* 

J *(*;*) 0.^(8 ; s,) e.^(t ; ,) (ds dt) 

and, from what has been said in the preceding paragraph, that portion of the latter 
which arises from the part of Q exterior to d n is zero, while that arising from </ u is 
simply 

[ K (s, t) (ds dt). 
Jn 
We have, therefore, 

f f K(s,t)0., 1l (s;s 1 )0. t ,(t;s l )d8dt 

J a J a 

= f K(*,t)(dsd*)+l K(M)^;*iK,(;*i)('fr< / 0- . . (2) 

Jg Jil 



Again the total area of d n is 4(2Tj + e), and so, if M is the maximum value of 
| K (s, t) \ in Q, we have 



If K(*,t)0. t ,(s;* l )0, i ,(t; 

I J <ln 

also the remaining integral on the right-hand side of (2) can be replaced by 

rs, + >i r^+Tj 

K: (.s' ; t) ds dt, 
"' '' 



wliich is evidently equal to 

f 7 * I" 1 

K (^i + u, s l + v) du dv. 

J -T) J -n 

Thus it follows from (2) that 
[ f K(s,t)0 tt .(s;s 1 )0 t M;s 1 )dsdt-F f K (s l + u,s l + v)dudv <4(27 ? + e)M. . (3) 

|JoJa J_,,J_, 

Now let us suppose it possible for K (s lt s^ to have a negative value, say a ; then, 
because K (s, t) is continuous, we can choose a value of 77 so small that 



for all values of u and v whose moduli are not greater than 17. We shall therefore 
have 



n n 

K(S I + U, St + v) du dv > 2r) 2 a. 

J - 



Recalling our hypothesis that K (s, t) is of positive type, it follows from this and 
(3) that 



Of. HOBSON, 'The Theory of Functions of a Keal Variable' (1907), p. 416. 



422 MK. J. MERCER: FUNCTIONS Of POSITIVE AND NEGATIVE TYPE, 

for all values of e which are less than a certain positive number ( 5). But this is 
evidently impossible, because, when e tends to zero, the right-hand side tends to zero, 
and we arrive at the contradiction that a fixed positive quantity (viz., rfa) is less 
than, or equal to, zero. 

We conclude that K (s l} i) cannot be negative when , lies in the open interval 
(a, b) ; and hence, since K (s, s) is continuous in the same interval when regarded as 
closed, we have the result that every function K (s, t) which is of positive type in the 
square a < s ^ b, :<& satisfies the inequality 

K ( *,) > 0* (a == ! < b). 

7. This is a first condition which must be satisfied by these functions, and we may 
obtain a second on similar lines. Let s, and tt a be any two distinct points of the open 
interval (a, b), and, as before, let e and 17 be two positive numbers ; the latter will now 
be supposed so small that the intervals [.s-, (r/ + e), *!+ (17 + e)], [$ 2 (r/ + e), s 2 + (>7 + e)] 
are both contained within (a, b) and do not overlap. We now propose to consider the 
values of the function 

[x.O^ (s ; Sl ) + x.A,, (* ; *)] OA, (t ; .s-,) + a- 2 0.., (t ; ,s 2 )] 

at points interior to Q, when x-i and x. 2 are any real constants. For this purpose we may 
make use of a diagram (tig. 2) which is an obvious extension of the one employed in 
the previous paragraph. The square Q is divided in this case not by eight, but by sixteen 
lines, viz., those whose equations are * = s a 77, .s- = ,v a + (77 + e) ; t = s ft + rj, t = s/, (77 + e) 
(a., ft = 1, 2). By giving a and /3 all possible values in the equations just written, it 
will be seen that we obtain four sets of eight, for each of which we can distinguish a 
square q^ bounded by the lines .s = ,s- a + T), t = .^ + ?? ; moreover, these squares will 
evidently have borders d^ of width e. It is not difficult to see that, in those parts 
of Q which are exterior to the borders d afi (a, ft = 1, 2), we have either 



or 



that in the square q afi we have 



* The reader may compare this with the fact that, when we have a quadratic form which only assumes 
non-negative values, and we put all the variables save one (say x^ equal to zero, we deduce that the 
coefficient of x-f must be > 0. 

t Both these pairs of equalities will hold in certain parts of the square, but we only require that at 
least one of them should be true. 



AND THEIR CONNECTION WITH THE THEORY OF INTEGRAL EQUATIONS. 423 

and that in the border d^ the last pair of equations still hold, but #,_, (s ; s a ), 6 ti1l (t ; s^) 
are each less than, or equal to, unity. From this it appears that the function 

[>i0.., (* ; *i) + a- A, (*' : s *)] M., (t > *i) + *A, (* : *)] = We in '//. (> = !. 2 )' 

= outside the borders d^, 
and that in the border d at3 its modulus is < | x^ 



dlf 



< 










u 

^f- 
n 



8. Let us now write 

e(s) = x 1 #, <1l (8',s 1 ) + x a e, in (s;s a ), 

for the sake of brevity. It follows from the remarks of the preceding paragraph that 

( j K (,v, t) 6 (s) 9 (t) ds dt = 2 2 x^Xp I K (s, t) (ds dt) 

= 1 ~ ? afl 

+ 2 2 f K (s,t)0(s)e(t)(dsdt). . . (4) 

a=l 8=1 Jrf a/3 

Now the area of each of the borders d^ is 4e(2^ + e), and so we have 
2 2 f K (s,t)e(s)0(t)(dsdt) 

o=l /J=l Id . 



424 MR. J. MERCER: FUNCTIONS OF POSITIVE AND NEGATIVE TYPE, 

moreover, it is easily proved that, in virtue of the symmetry of K (s, t), 

22 r 

2 2 x^Xf, K (s, t) (ds dt) 

a=l /3 = 1 Jj a 

can be written as 

T r f r, a K (s, + u s, + v) + 2x^x 2 K (s , + , s 2 + v) + X/K (s 2 + u,s 2 + v\] dudv. . ( 5 ) 

L i \ i i j / \ * / \ /-i \ / 

J 7J J V) 

From this and the equation (4) we finally obtain the inequality 

r* f* P 1 f" 1 \ ? 2 

, J /I J T) */ TJ 



where F 2 (w, v) is the integrand of (5). 

The function F 2 (u, v) is, of course, dependent on the real constants x l and x 2 ; let 
us suppose it possible to choose them in such a way that 

F,(0, 0) = a-A^i, *0 + 2x 1 x 2 *(s l , s 2 ) + x 2 2 K (s 2 , s 2 ) 

takes a negative value, say ft. Owing to the fact that K (s, t) is continuous, it is 
then clear that we can chose rj so small that 



for u S 17, | v ^ r). From this we deduce the inequality 



as in the corresponding place in 6 ; and hence, as this is impossible for sufficiently 
small values of e, it follows that, when y 1 and s 2 lie in the open interval (a, 6), and x l 
and x 2 are real, F 2 (0, 0) is not negative. Accordingly, since K (s, t) is continuous, it is 
easily seen that every function K (s, t) which is of positive type in the square a < s ^ b, 
a ^ t < b is such that, when x { and x 2 are any real numbers, 

~ Si ~ 



X\K (Si, $l) + ZX&K ($!, S 2 ) + X/K (S 2 , S 2 ) > ( a ~ Si ~ , ) . 

V 'A/ 03 U J 

9. The reader will now be prepared for a general theorem of which those already 
considered are particular cases. After having been through the latter in detail it will 
be sufficient to sketch the general proof. 

Take any n distinct point s l} s s ,...,s n in the open interval (a, b), and suppose that e 
and 17 are so small that the intervals [s a (i? + e), s a + (^ + e)] (a = 1, 2,...,) form a 
non-overlapping set contained within (a, b). Now let 

6(8)= $x a 8^(s;s a ), 



AND THEIR CONNECTION WITH THE THEORY OF INTEGRAL EQUATIONS. 425 



where x lt x 2 , ..., x, t are any real constants; and consider the values of the function 
6 (,s) (f) in Q. It will be seen on consideration that in this general case Q must be 
regarded as divided by 8n lines, and that there are n 2 squares q^, each having a 
border d^ (a, /8 1,2,..., n). It will also be seen that 

0(*)0(t) = X& in ^ (, = 1, 2,..., n), 
outside the borders d afi , 

and that in the border d ai we have 



afi 



Proceeding then as in the case n = 2, we obtain the inequality 



where 



j K (.s, t) 6 (.s) (t) ds cfc-J 1 |" F. (u, v) du do < 4e (2y? + e) ( S 



.'/' i 



M, 



F n (, r) = X?K (! + , Sj + r)+ .r/K (s, + u, .s- 2 + r) + . . . + .'/: (* + , ,v,, + /) 



and hence we establish that F n (0, 0) is always > 0. Eventually we obtain the 
general theorem : 

Every function K (x, t) which is of positive type in the square a^.^^h, ct^f^b 
must be such that, when s lt s 2 , ..., s n are any points of the closed interval (a, b), we 

have 

X?K (.s- 1; s 1 ) + .r.j*K (*,, -s- a ) +...+.</: (s n , s n ) + '2,A\.v., K (.s- 1; s,)+ ... > 0, 

for all real values of x l} x 2 , ..., :r H . 

1 0. In accordance with the notation employed by FREUHOLM, let 



K (, A'j) /C (*', 6-3) ... K (*, A',,) 

Then, by the theory of quadratic forms, it is known that, in virtue of the inequality 
which has just been obtained, we must have* 



(6) 



* Vide BROMWICH, 'Quadratic Forms and their Classification by means of Invariant Factors' (1906), 
pp. 19, 20. 

VOL. CCIX. A. 3 I 



426 MR. J. MERCER: FUNCTIONS OF POSITIVE AND NEGATIVE TYPE, 

and this is true independently of the number of points, s u s 2 , ...,s n and their situation 
in the interval (a, b). 

Conversely, by an appeal to the theory of integral equations, we may prove that 
any continuous symmetric function K (s, t) defined in Q, which satisfies this condition, 
is of positive type. For it will be remembered that, according to FREDHOLM'S 
theory,* the singular values of the equation 



t ........ (7) 

J a 

are the zeros of the integral function 

D(X)= 1-xf *(*,) rf*i+ f l**^ 1 '*')*^,... 

J /i : J a . a \"1) J/ 



Applying our hypothesis that (G) holds for all values of ,<?,, ,s 2 , ..., $, it appears that 

C XV' 
the coefficient of ' f- in the series on the right cannot be negative ; moreover, 

tL ; 

HILBKUT has proved that every continuous symmetric function has its singular values 
all real. It follows, therefore, that, if X,. is any one of the zeros of D (X), we shall 
have 



where the series in the square brackets on the left is not negative and that on the 
right is positive ; and hence, that X r must be positive. Since we have seen that, for 
K (,s, t) to be of positive type, it is sufficient that all the singular values of (7) should be 
positive, we may now state the following theorem : 

In order that a continuous symmetric function K (s, t) defined in the square 
a<s<6, a-^t^l may be of positive type, it is necessary and sufficient that the 
functions 



should never take negative values when the variables s lt s 2 , ..., s n ... each range over 
the closed interval (a, b). 

* Fide 'Acta Mathematical XXVII (1903). 



AND THEIR CONNECTION WITH THE THEORY OF INTEGRAL EQUATIONS. 427 

It may be remarked that, as a corollary of this theorem, we have the notable fact 
that, if any continuous symmetric function is such that the integrals 

r* c b r* / \ r* r* r* /e e <> \ 

K ( 8l , Sl )d8 1 ,\ *(*'*') <&,<&,,..., I ... K ( Si > s *-> s ")d Sl d S2 ...ds n ,... 

Jn JaJn \*li *2/ J a J a J a \ S l, 2> > S n/ 



are none of them negative, then the functions (8) have the same property. 

11. The properties of the determinants (8) may be used to obtain some idea of the 
nature of functions of positive type. Let us suppose, in the first place, that there is 
a point (a^ i) belonging to Q at which one of these functions K (s, t) vanishes. The 

determinant K('' M evidently reduces to \_K(S, i)] 2 ; hence, because it can never 

be negative, 

(*, a,) = K (a l , ft) = 0. 

In other words, if we draw the square Q and the diagonal s t, the existence of a 
point (j, j) on this diagonal at which K (.s', f) vanishes involves the fact that K (*, t) 
vanishes everywhere on the lines drawn through this point parallel to the axes of .s- 
and t. In particular, we deduce from this that a function K (.s, t) which is of posit ire 
type, and is not zero everywhere in Q, cannot vanish everywhere on the diagonal s = t. 

More generally, let us suppose that there are points a,, a l} ..., a n of the interval 
(a, b) such that 

, a a , ..., a n \ 



\a t , a.,, ..., a 



By considering the determinant whose elements are the first minors of the four 
elements belonging to the first two rows and columns of 



*, ,, a,, ..., a n 



, ,, ,, ..., n (1Q) 

\8, a 1; a 2 , ...,/' 

we obtain the equation* 



K s, i, a a , ..., a n K /a 2 , a 3 , ..., a n 
\s, a,, a 2 , ..., aj \a 2 , a s , ..., a n 



= K /S, a,, ..., n \ K (a 1 , a.,, ..., a n \ _ f /, a , -., n \l 2 
\s, a 2 , ..., aj \a 1} a 2 , ..., aj \ 1; a 2 , ..., aj] 



Recalling that the first term on the right vanishes in virtue of our hypothesis, and 
that neither of the terms in the product on the left can be negative, it is clear that 
we have 

s, a,, ..., a n \ 






* Vide SCOTT and MATHEWS, ' Theory of Determinants' (1904), p. 62. 

3 I 2 



428 ME. J. MERCER: FUNCTIONS OF POSITIVE AND NEGATIVE TYPE, 

at each point of the interval (a, b) ; and it can be proved in a similar way that the 
remainder of the functions 



, a a , .... a r _,, *, 

fv ti n ri 

U\, a 2 , ..., (*r- 1) w r 



,, ..., a n \ / = l 2 n ) . . . . (ll) 

ft I * ' * * 



have the same property. 

Again, because the determinant (9) and the functions (l 1) all vanish, it is easily 
seen that the function (10) vanishes identically. Accordingly, if any one of the 
functions (8) vanishes for all values of the variables, so must all those which follow it. 
it appears, therefore, that, when K (s, t) is of positive type, the determinant of the 
integral equation (7) is either an infinite power series in X whose coefficients are 
alternately positive and negative numbers, or else it is a polynomial whose coefficients 
obey the same law. 

Another property which is worth noticing is that, if L is the upper limit of the 
function (*, *) in the interval (ri, b), then 



in the whole of the square Q. This follows immediately from the fact that, since 



we have 



12. We have so far confined ourselves to the consideration of functions of positive 
type, but the reader will easily perceive that the results obtained for these functions 
may be made applicable to those of negative type by a simple device. In fact, if 
K(.S V , ) is of negative type in the square Q, and we suppose that 



it is evident that K (s, t) is of positive type in Q. Applying then what we have said 
about functions of positive type to K' (s, t), we may deduce the analogous properties of 
K (s, t); for instance, the necessary and sufficient condition that a continuous symmetric 
function K (s, t) defined in tJie square a^s^b, a^t^b may be, of negative type is 
that the functions 



should never be negative when the variables s l} s 2 , ..., s n , ... each range over the closed 
interval (a, b). 

We may remark that this result and that of 10 prove the classes of functions of 



AND THEIE CONNECTION WITH THE THEORY OF INTEGRAL EQUATIONS. 429 

positive and negative types to be mutually exclusive, save for the trivial case when 
K (s, t) vanishes everywhere. For, if K (s, t) belongs to both classes, we must have 



for all points of the interval (a, b) ; and hence *(.<?,, s,) must be zero everywhere in 
this interval. It follows, then, from a remark made in 11, that K(.S, t) is zero in the 
whole square Q. 

PART III. CERTAIN FUNCTIONS OF POSITIVE TYPE. 

13. In the present section we propose to investigate certain species of functions 
which are of positive type. The remark made at the end of the previous section 
( 12) will make it plain that there is no loss in thus limiting ourselves, since the 
corresponding results for functions of negative type may be at once deduced by the 
device there explained. 

Let us again consider the square Q of the (x, t) plane which is bounded by the lines 
<t = a, s = b, t a, t = b ; and let us suppose that it is divided into two triangles by 
the diagonal whose equation is s = t. The most direct method of denning a continuous 
symmetric function in Q is, evidently, to define a continuous function in one of the 
triangles, say that in which N < / ; and then to suppose this continued into the 
remaining portion of the square by defining its value at a point for which .s- > t to be 
that at its image by reflection in the diagonal. For example, if 9 (,s) is a continuous 
function of s in the interval (ft, b), and we define K (.s, t) to be equal to 9 (s) in the 
triangle .s ^~ t, then the continuation of this function into the triangle .s > t is 
evidently 9 (t}. 

The theorem of 10 may be applied to the function we have just defined, and hence 
the condition that it should be of positive type deduced. Instead of doing this, 
however, we shall consider the more general function* 

(,<)-'()*(') (**t) 

*()*(*) (.a). 

where 9 (s) and 4> (>">') are both continuous in the interval (a, b). It will be remembered 
that functions of this kind occur as GREEN'S functions of certain linear differential 
equations of the second order, and that it is therefore of some interest to know when 
they are of positive type. Accordingly we shall seek necessary and sufficient 
conditions which will ensure that this is so. 

14. In the first place, let us suppose that 6 (s) and < (s) are any continuous 
functions whatever ; and let 2 be the set of points belonging to (a, b) at which 
neither of them vanish. This set will evidently be dense in itself in virtue of the 

* Of. BATEMAN, ' Messenger of Mathematics,' New Series, 1907, p. 93. 



430 ME. J. MERCER: FUNCTIONS OF POSITIVE AND NEGATIVE TYPE, 

continuity of the functions ; but it cannot be closed, unless it contains every point of 
the interval. Moreover, it can be proved that a and ft, its lower and upper limits 
respectively, do not belong to the set, unless they coincide with the end points of the 
interval. 

At each point of the set 2 the quotient 



will have a definite value, because </> (.v) is never zero. We may therefore define a 
single-valued function f(*), whose domain is 2, and whose value at any point is that 
of this quotient. It will appear in the sequel that the properties of K(S, t) depend 
very largely on the nature of f(s), and accordingly, in anticipation of this, we shall 
speak of it as the discriminator of K (.v, t). T lie discriminator will evidently be 
continuous in its domain, but it will never have the value zero. 

15. Let us now suppose that K (.s-, t) is of positive type, and is not zero everywhere 
in the square Q. We have proved ( 11) that, under these circumstances, the function 
*(*!< ' s 'i), which in the present case is simply (&i) (f> (sj, cannot be zero in the whole 
of (>, />); also, at points where it does not vanish, we know that K(SI, s^ is positive 
(6, 10). It follows that, for a function of positive type, the set 2 certainly exists, 
and that in it the discriminator only takes positive values. 

Again, when N L and .s- 3 are any two points of ^, and ft., > .v,, we have 



hence, since /'(*,) is a positive number, it follows by the theorem of 10 that 



This result may be combined with the previous one in the statement that the 
discriminator of /c(.v, /) is a non-decreasing function whose values are all positive. 

We have next to consider the points of (a, b) at which one or both of the functions 
6 (.s-), </> (x) vanish. These fall naturally into three sets, according as they belong to 
(1) the closed interval (a, a), (-2) the closed interval (ft, 1>), or (3) the open interval 
(a, ft). As regards (l), it is not difficult to show that (s) vanishes in the whole 
interval. For, if a, is any point of (K, a), one at least of the numbers (%), < (oj) 
must tie zero ; and hence, since K (a ]; a^ is zero, the function K (s, a t ) is zero at each 
point of (a, b) (11). 

Now when s > c^ we have 

K (s, ((l ) = (a,} 4> (s), 

and, at points of 2, $ (s) does not vanish ; we must therefore have (a^ = 0. It can 
be proved in a similar manner that <f> (s) vanishes everywhere in the interval (ft, b). 

Finally, we can show that, at points of the open interval (a, ft) which do not belong 
to 2, both (s) and <f> (s) vanish. In fact, if a t is any one of these points, there are 



AND THEIE CONNECTION WITH THE THEOKY OF INTEGRAL EQUATIONS. 431 



clearly points of 2 both on its right and on its left. The argument we have just 
employed will then establish that, by reason of the former, 6 (j) is zero, and that, 
by reason of the latter, <(i) is zero. 

1 6. Conversely, let us suppose that K (s, t) is defined in terms of continuous 
functions 6 (s), <fr (.s - ) which have the properties mentioned in the preceding paragraph ; 
and let us consider the function 



1, S 2 , 



(12) 



where $1, s 2 , ... , s n are variables each confined to the interval (a, V), We may remark 
that, as this function is symmetric, it will take all possible values iu the domain 
Si S A - 2 ^ iV 3 < ... < ts n . Thus, since we are only concerned with the sign of the function, 
we may always siippose the variables to satisfy these inequalities. Firstly, let us 
suppose that one of the variables has a value not belonging to the domain of the 
discriminator of K (H, t). If such a value belongs to (a, a), the point s 1 must evidently 
lie in this interval ; hence, since 

K(*I,*,) = (*i) <!> (O (r = l,2,....,n), 

and 6 ((<i) vanishes by our hypothesis, it is evident that all the elements of the first 
row of (12) are zero. In a similar manner it may be proved that, when one of the 
variables has a value belonging to the interval (b, /8), all the elements of the last row 
vanish. Again, if one of the variables, say ,, has a value belonging to the open 
interval (a, /3), but not to 2, we shall have 

K) = < (") = o 

by our hypothesis. It is thus easily seen that the elements of the m th row of (12) all 
vanish. Summing up our results so far, we conclude that the function (12) can only 
take values different from zero when the variables s l} ^, ... , # are each confined to 
the set 2. 

17. Let us next consider the case when the variables are restricted in this manner. 
The function (12), when expressed in terms of the functions 6 and <f>, is 



e (*,) * (*,), e (*) 

8 (s>) + (*,), 8 (,)<!>(*,), 

8 ( 



*(,)*(*.). *(*)*(), 



< S n ), 



432 MR. J. MERCER: FUNCTIONS OF POSITIVE AND NEGATIVE TYPE, 

hence, by dividing through both the r th row and the r th column of this determinant 
by < (s r ) (r = 1, 2, ..., n), its value is seen to be 

>i)^(* 8 )--^(*.) 

/(*,),/(,), ../(*) 



/(.s-,), /(,), ...,/(*) 

The determinant just written can be evaluated without difficulty, and thus we find 
that (12) is 



Now, according to our hypothesis, /'(*,) is positive and each of the factors 
[/'(*) /'(- s '-i)] is positive or zero, It follows, then, that (12) cannot take negative 
values when the variables are each restricted to the set 2. Taking this in conjunction 
with what was said in the previous paragraph, we see that the functions 



/ \ / 01, 03 i / oj, 2, ..., o n 

K (* i '^'' t UM/" t "U! ,!"',*". 

can never take negative values, when the variables ,S'j, s. 2 , ..., s n , ... each range over 
the interval (ft, b), and hence, by the theorem of 10, that K(S, t) is of positive type. 
We may, therefore, state our results in the following theorem : 

If 0(x) and (/>(*) are each continuous functions defined in the interval (a, b), the 
necessary and sufficient conditions that the function 



should be of 'positive type are (l) /w <Ae discriminator of the function should be 
positive and non-decreasing in its domain S, and (2) /ja, ^y a and ft are the lower 
and upper limits of S, 6 (s) should be zero in the interval (a, a), < (s) zero in the 
interval (/S, b), and both B(s) and <f>(s) zero at points of the open interval (a, /3) which 
do not belong to S. 

As a corollary of this, by supposing that (f> (s) = 1 (a < s < b), the reader may 
deduce the corresponding conditions for the function defined in 13. 

1 8. Let us now investigate under what circumstances a function K (s, t), which 
satisfies the conditions stated in the enunciation of the theorem of 17, is definite. 
If the domain of its discriminator is not dense everywhere, it will be possible to find 



AND THEIR CONNECTION WITH THE THEORY OF INTEGRAL EQUATIONS. 433 

an interval (c, d), lying within (a, b), such that at each of its points the function 
B(f<i) <f>(*i) is zero. We shall, therefore, have (11) 

K (.<?, t) = (c < s : d, a^t^. b) 
= (c^t^d, a < .s> < 6) ; 

in particular, K (s, t) will vanish everywhere in the square c ^ s ^ d, c ^ t < d. 
Now, if x () is an y continuous function of ,s- defined in the interval (a, b), which is 
zero in the intervals a ^ s < c, (/ < .s- S fr, hut does not vanish everywhere in (c, d), 
we shall have 

* (, x (*) x (0 <i* * = I* * (*, x (*) x (0 ** dt 



by the properties of ^(.s) and K(.S-, i). It follows from this that, if K(S, t) is definite, 
the domain of its discriminator must be dense everywhere in (a, b). 

Again, let us suppose that the discriminator of (*, t) lias a constant value p 
throughout a certain interval (c, d). It will then be seen that within the square 



and hence, if x (*) is defined as before, that 

f f * (*, X (*) X (0 da dt = !> \\ d + () x (,} c/.sT. 

J a Ja l_Jc J 

It may be proved without difficulty that there exists a function x (.s) which is not 
everywhere zero, and is such that 

WX*-0 .......... (13) 



For, let Xi ( s ) and